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ECONOMIC  CYCLES:  THEIR  LAW 
AND  CAUSE 


THE  MACMILLAN  COMPANV 

NEW    YORK    •    BOSTON    •    CHICAGO    •    DALLAS 
ATLANTA    •    SAN    FRANCISCO 

MACMILLAN  &  CO..  Limiteo 

LONDON    ■    BOMBAY    •   CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA.  Ltd. 

TORONTO 


ECONOMIC  CYCLES:  THEIR 
LAW  AIVD  CAUSE 


BY 
HENRY   LUDWELL  MOORE 

PROFESSOR  OF  POLITICAL  ECONOMY  IN  COLUMBIA  UNIVERSITY 
AUTHOR  OF   "  LAWS  OF  WAGES  " 


"  Nous  croyons  en  effet,  pour  notre  part,  que 
pour  avancer  vraiment  dans  la  connaissance 
4conomique,  il  faut  s'attaquer  directement  et 
d'abord,  a  des  variations,  c'est-a-dire  a  la  forme 
dynamique  des  ph6nomenes,  par  la  voic  ex- 
perimentale."  FR.-VNgois  Simiand. 


Nruj  f  nrk 

THE  MACMILLAN  COMPANY 

1914 

All  rights  reserved 


COPTRIOHT,    1914 

By  the   MACMILLAN  COMPANY 
Published  December,  1914. 


TO 

JANE   MOORE 

A  CRITIC  WHO   NEVER  DISHEARTENS 
A  CO-WORKER   WHO    KEEPS  THE   FAITH 


CONTENTS 

CHAPTER  I 
Introduction 1 

CHAPTER  II 

CYCLES   OF   RAINFALL 

The  Use  of  Fourier's  Theorem 6 

Periodogram  of  Rainfall 14 

The  Equation  to  the  Rainfall  Curve 21 

Rainfall  in  the  Corn  Belt 26 

CHAPTER  III 

RAINFALL    AND    THE    CROPS 

The  Secular  Trend  in  the  Yield  of  the  Croi)s 35 

Critical  Periods  of  Growth 41 

Cycles  in  the  Yield  of  the  Representative  Crops  and  the 

Corresponding  Cycles  of  Rainfall 44 

Cycles  in  the  Index  of  Crop  Fluctuations  and  in  the  Corre- 
sponding Index  of  Mean  Effective  Rainfall 49 

CHAPTER  IV 

THE    LAW    OF   DEMAND 

The  Tlicory  of  Demand 02 

Statistical  Laws  of  Demand GO 

The  Prediction  of  Prices 77 

Elasticity  of  Demand 82 

vii 


viii  Contents 


CHAPTER  V 

THE    .MECHANISM    OF   CYCLES 

The  Pri(;es  of  Agriculturul  Conunoditios  Correlated  with  the 

Yield  of  the  Several  Crops 94 

Rising  and  Falling  Prices  as  Related  to  Yield-Price  Curves     .  100 

The  "N'olunie  of  the  Crops  and  the  Activity  of  Industry      .     .  108 

A  New  Type  of  Demand  Curves 110 

The  Fundamental,  Persistent  Cause  of  Economic  Cycles   .     .  116 


CHAPTER  VI 

SUMMARY   AND    CONCLUSIONS 135 


ECONOMIC  CYCLES:  THEIR  LAW 
AND  CAUSE 


CHAPTER   I 
INTRODUCTION 

There  is  a  considerable  unanimity  of  opinion  among 
experts  that,  from  the  purely  economic  point  of  view, 
the  most  general  and  characteristic  phenomenon  of  a 
changing  society  is  the  ebb  and  flow  of  economic  life, 
the  alternation  of  energetic,  buoyant  activity  with  a 
spiritless,  depressed  and  uncertain  drifting.  During  the 
creative  period  of  the  rhythmic  change  each  factor  in 
production  receives  an  augmenting  income,  and  the 
mutual  adjustment  of  interests  in  the  productive 
process  is  brought  about  in  a  natural  w^ay,  primarily 
through  the  operation  of  competitive  law.  The  period 
of  decline  in  the  cycle  presents  a  sharply  contrasted 
aspect  of  industry.  With  the  organization  of  capital 
and  labor  at  first  unchanged,  the  amount  of  the  product 
falls;  each  of  the  interested  factors  seeks  at  least  to 
retain  its  absolute  share  of  the  product;  friction  and 
strife  ensue  with  a  threatening  of  the  disruption  of 
industry.  What  is  the  cause  of  this  alternation  of 
periods  of  activity  and  depression?  What  is  its  law? 
These  are  the  fundamental  problems  of  economic 
dynamics  the  solution  of  which  is  offered  in  this  Essay. 

Political  Economy  began  to  make  progress  in  a 
rational  way  when  the  Physiocrats  put  forth  their 
doctrine  of  the  dependence  of  all  forms  of  economic  life 

1 


2  Economic  Cycles:  Their  Lmv  and  Cause 

upon  agriculture.  Another  momentous  step  was  taken 
in  the  direction  of  theoretical  development  when  the 
English  economists  formulated  the  law  of  diminishing 
returns  in  agriculture  and  traced  its  all-pervasive 
influence  in  the  production  and  distribution  of  the 
product  of  industry.  The  desideratum  of  economic 
dynamics  at  the  present  time  is  the  discovery  of  a  law 
that  shall  be  to  a  changing  society  what  the  law  of 
diminishing  returns  in  agriculture  is  to  a  society  in  a 
comparatively  static  condition. 

The  full  truth  in  the  old  Physiocratic  doctrine  has 
not  been  exploited.  The  Department  of  Agriculture 
of  the  United  States  reaffirms  the  central  idea  of  the 
doctrine  in  its  motto:  ''Agriculture  is  the  Foundation 
of  Manufacture  and  Commerce,"  and  in  the  spirit  of 
this  motto  it  publishes  invaluable  statistical  data. 

It  is  proverbial  that  the  farmer  is  at  the  mercy  of  the 
weather.  If  it  be  true  that  the  explanation  of  economic 
cycles  is  to  be  found  in  the  law  of  supply  of  agricultural 
products,  it  is  surely  wise  in  a  study  of  rhythmic  eco- 
nomic changes  to  inquire  whether  the  law  of  the  chang- 
ing supply  of  raw  material  is  not  associated  with  a  law  of 
changing  weather.  Is  there  a  well-defined  law  of  chang- 
ing weather? 

Supposing  that  it  is  possible  to  discover  that  the 
weather  passes  through  cycles  of  definite  periods  and 
definite  amplitudes,  it  will  then  be  necessary  to  show 
how  the  crops  are  affected  by  the  weather  and  how  the 
cycles  of  the  weather  are  reproduced  in  cycles  of  the 
yield  of  the  principal  crops. 


Introduction  3 

Wlien  the  changes  in  the  physical  yield  of  the  crops 
are  shown  to  be  dependent  upon  changes  in  the  weather, 
the  next  stage  in  the  investigation  is  to  connect  the 
yield  with  its  value,  and  this  brings  one  face  to  face 
with  another  unsolved  problem  in  theoretical  economics. 
The  most  recent  phase  of  economic  theory  opens  with  a 
description  of  the  ''law  of  demand,"  which  from  the 
time  of  Cournot,  Dupuit,  and  Gossen  has  been  assumed 
in  all  theoretical  discussions,  but  there  has  been  no 
method  for  finding  the  statistical  equation  to  the  law. 
It  will  be  necessary  to  overcome  the  difficulties  of  this 
problem  before  a  solution  can  be  offered  of  the  more 
fundamental  inquiry  as  to  the  law  and  cause  of  cycles  in 
economic  phenomena. 

When  the  physical  yield  of  the  crops  has,  on  the  one 
hand,  been  related  to  the  cycles  of  the  weather  and,  on 
the  other,  to  the  prices  of  the  respective  crops,  it  will 
then  be  possible  to  take  the  final  step  and  to  show  how 
the  cycles  in  the  physical  yield  of  the  crops  produce  the 
cycles  in  the  activity  of  industry  and  the  cycles  of 
general  prices,  and  how,  finally,  the  law  of  the  cycles  of 
the  crops  is  the  law  of  Economic  Cycles. 


CHAPTER   II 

CYCLES  OF  RAINFALL 

"The  first  thing  that  in  my  opinion  ought  to  be  done  towards 
making  the  observations  useful  for  scientific  purposes  is  to  perform 
that  kind  of  more  perfect  averaging  which  is  afforded  by  the  har- 
monic analysis.  There  is  a  certain  amount  of  averaging  done,  but 
that  is  chiefly  daily  averages,  with  monthly  averages,  and  yearly 
averages;  but  the  more  perfect  averaging  of  the  harmonic  analysis 
would  give  the  level  of  the  variation  of  the  phenomenon." 

— Lord  Kelvin,  in  his  testimony  before  the  Meteorological  Com- 
mittee of  the  Royal  Society,  1876. 

From  the  point  of  view  of  the  relation  of  changing 
weather  to  the  varying  fruitfulness  of  agriculture,  the 
most  important  factors  that  are  usually  included  in 
the  term,  weather,  are  temperature  and  rainfall.  We 
begin  our  investigation  with  this  common  belief  and 
inquire,  in  this  chapter,  whether  the  varying  amount 
of  annual  rainfall  is  subject  to  any  simple  law. 

In  order  to  carry  forward  the  inquiry  as  to  the  exist- 
ence of  a  law  of  annual  rainfall  an  analysis  must  be 
made  of  a  long  record  of  precipitation.  Our  choice  of 
a  record  is  limited  by  two  conditions:  First,  our  object 
in  investigating  the  periodicity  of  rainfall  is  the  hope 
of  throwing  light  upon  the  periodicity  in  the  yield  of 
the  crops,  and  this  expectation  obviously  makes  it 
desirable  that  the  record  of  rainfall  shall  be  as  repre- 
sentative as  possible  of  the  conditions  of  precipitation 

4 


Cycles  of  Rainfall  5 

in  our  leading  crop  area;  secondly,  as  the  existing 
meteorological  records  are  of  unequal  lengths  and  of 
varying  reliability,  it  is  necessary  to  take  the  best  long 
records  that  can  be  found  within  the  limits  of  the  crop 
area. 

The  principal  region  of  grain  production  in  the  United 
States  is  in  the  Mississippi  Valley,  but  the  meteoro- 
logical records  of  the  Middle  West  do  not  extend  through 
a  long  period  of  time.  In  order  to  achieve  the  two  ends 
of  having  a  long  record  of  precipitation  and  of  having 
the  record  typical  of  the  conditions  in  the  grain  area, 
the  device  has  been  adopted  of  investigating  rainfall  in 
the  Ohio  Valley — which  affords  the  longest  record  ob- 
tainable in  the  neighborhood  of  the  central  Mississippi 
region — and  of  showing  that  the  rainfall  of  our  lead- 
ing grain  state,  Illinois,  follows  the  same  law  as  the 
rainfall  of  the  Ohio  Valley. 

The  stations  in  the  Ohio  Valley  with  long  rainfall 
records  are  Marietta,  Portsmouth,  and  Cincinnati. 
Their  mean  annual  rainfall  since  1839  is  given  in 
Table  I  ^  of  the  Appendix  to  this  chapter.  The  graph 
of  the  course  of  rainfall  in  the  Ohio  Valley  since  1839 
is  traced  with  other  graphs  on  Figures  4,  5,  and  6.  The 
problem  that  must  now  be  faced  is  the  question  as  to 
whether  the  sequence  of  annual  rainfall  in  the  Ohio 
Valley  follows  a  simple  law,  and  if  so,  to  give  a  quanti- 
tative formulation  of  the  law. 

1  The  data  were  taken  from  Bulletin  W  of  the  Weather  Bureau  of 
the  United  States  and  from  the  Annual  Reports  of  the  Chief  of  the 
Weather  Bureau. 


6  Ecojiomic  Cycles:  Their  Law  and  Cause 

The  Use  of  Fourier^ s  Theorem 

A  preliminary  examination  of  the  rainfall  data  of  the 
Ohio  Valley  leads  to  the  conclusion  that  there  is  prob- 
ably no  secular  trend  to  the  data,  that  is  to  say,  there 
is  probably  no  tendency  of  the  rainfall  to  increase  con- 
tinuously or  to  decrease  continuously  with  the  flow  of 
time.  It  is  true  that  when  the  amount  of  rainfall  is 
correlated  with  time,  the  coefficient  of  correlation  is 
r  =  —  .227  ±  .075,  where  the  coefficient  is  three  times  its 
probable  error  and  is  therefore  suggestive  of  a  decrease 
in  the  amount  of  rainfall  with  the  flow  of  time.  More- 
over, if  a  straight  line  is  fitted  to  the  data,  the  indicated 
annual  decrease  in  the  rainfall  is  seven  hundredths  of 
an  inch.  But  these  facts  are  no  justification  for  hold- 
ing to  a  secular  decrease  in  the  amount  of  annual 
rainfall.  For,  in  the  first  place,  if  there  are  cycles  in 
the  amount  of  the  rainfall,  the  low  degree  of  the  ob- 
served correlation  might  be  due  to  the  data  of  rainfall 
including  incomplete  cycles;  in  the  second  place,  the 
record  is  drawn  from  only  three  stations  and  because 
of  the  limited  number  of  stations  might  give  an  acciden- 
tal, low  degree  of  correlation  between  amount  of  rain- 
fall and  time;  and  in  the  third  place,  improvements 
in  the  method  of  taking  the  observations  might  have 
introduced  changes  that  would  account  for  the  ob- 
served small  annual  decrease  in  the  amount  of  rain- 
fall. In  view  of  these  considerations,  it  is  probably 
best  to  proceed  with  our  problem  on  the  assumption 
that  there  is  no  secular  trend  in  the  amount  of  annual 


Cycles  of  Rainfall  7 

rainfall.  If  this  assumption  is  true,  it  follows  that,  in 
all  probability,  the  course  of  rainfall  in  the  Ohio  Valley, 
is  cyclical,  or  a  combination  of  cycles. 

In  an  inductive  treatment  of  any  form  of  rhythmic 
or  cyclical  change  it  is  necessary  that  the  method 
adopted  shall  satisfy  two  conditions:  (1)  It  shall  be 
consistent  with  recognized  mathematical  processes; 
(2)  It  shall  afford  means  of  testing  the  degree  of  proba- 
bility that  the  results  are  not  chance  phenomena. 
Unless  the  method  rests  clearly  upon  an  approved 
mathematical  process,  it  is  scarcely  possible  to  say 
whether  the  attained  results  may  not  be  entirely  formal ; 
and  unless  the  findings  are  tested  for  the  degree  of  their 
probability,  there  is  no  assurance  that  the  adduced 
cycle  may  not  be  a  chance  occurrence.  The  literature 
in  which  rhythmic  phenomena  are  treated  in  a  statis- 
tical way  teems  with  fallacies  and  uncertainties  that 
illustrate  the  need  of  observing  the  above  conditions; 
for  the  method  frequently  adopted  of  smoothing  the 
data  is  so  arbitrary  that  one  is  at  a  loss  to  know  whether, 
after  all,  the  alleged  periodicity  may  not,  in  fact,  be  due 
to  the  process  of  smoothing;  and,  in  addition,  one  is 
left  in  doubt  as  to  whether  an  indefinite  number  of 
cycles  other  than  the  particular  one  adduced  might  not, 
with  equal  or  greater  probability,  be  obtained  from  the 
same  data. 

The  method  that  was  employed  to  reach  the  results 
of  this  chapter  rests  upon  the  analysis  invented  by 
Joseph  Fourier,^  which  is  called,  in  English  treatises, 

'  The   most   philosophic  exposition  of   Fourier's   tlieoreni   is   in 


8  Economic  Cycles:  Their  Law  and  Cause 

harmonic  analysis.  The  perfection  of  the  method 
whereby  the  findings  may  be  subjected  to  the  test  of 
probabiUty  is  the  work  of  Professor  Arthur  Schuster  ^ 
of  Manchester. 

We  may  begin  the  presentation  of  the  method  with  a 
definition  of  a  series  of  terms  that  constantly  recur  in 

the  treatment  of  periodic  phe- 
nomena. Figure  1  will  facili- 
tate the  exposition  by  affording 
a  graphic  description  of  the 
terms  dealt  with. 

Suppose    that    the    pomt   Q 
moves  uniformly  in  the  circle 
of  Figure  1 ,  that  is  to  say,  sup- 
'^^^^    ■  pose  that  the  point  Q  describes 

equal  arcs  in  equal  times  and,  therefore,  proportional 
arcs  in  different  times.  Then,  if  the  measurements  of 
the  arcs  of  the  circle  are  made  from  the  point  A  and 
the  reckoning  of  time  is  begam  when  Q  is  at  E,  the 
angle  A  O  E  w>  called  the  angle  at  epoch,  or  simply 

Fourier's  own  work:  Theorie  analytique  de  la  chaleur.  In  Freeman's 
English  translation  the  treatment  is  found  on  pp.  137-212. 

^  The  fundamental  memoirs  of  Professor  Schuster  are 

"On  the  Investigation  of  Hidden  Periodicities  wdth  Application 
to  a  Supposed  26  Day  Period  of  Meteorological  Phenomena." 
Terrestrial  Magnetism  for  March,  1898. 

"The  Periodogram  of  Magnetic  DecUnation  as  obtained  from  the 
records  of  the  Greenwich  Observatory  during  the  j-ears  1871-1895." 
Cambridge  Philosophical  Society  Transactions,  Vol.   18,   1899. 

"On  the  Periodicity  of  Sunspots."  Philosophical  Transactions  of 
the  Royal  Society  of  London,  A,  Vol.  206,  1906. 

"The  Periodogi'am  and  its  Oi)tical  Analog}'."  Proceedings  of 
the  Royal  Society  of  Lo'ni!<))t,  A,  'N'oL  77,  1906. 


Cycles  of  Rainfall  9 

the  epoch  of  the  uniform  circular  motion.  The 
radius  of  the  circle  is  the  amplitude  of  the  motion; 
the  time  of  going  once  around  the  circle  is  the 
period  of  the  motion;  the  ratio  of  A  Q  to  the 
circumference  of  the  circle  is  the  phase  of  the  mo- 
tion. 

If  from  each  position  of  Q  a  perpendicular  is  dropped 
upon  the  diameter  of  the  circle,  G  H,  the  foot  of  the 
perpendicular  will  describe  a  simple  harmonic  motion. 
The  amplitude  of  the  simple  harmonic  motion  is  one- 
half  of  the  range  of  the  motion,  that  is,  one-half  of  G  H, 
or  the  radius  of  the  circle.  The  period  of  the  siinple 
harmonic  motion  is  the  interval  between  the  passing 
of  the  point  P  twice  through  the  same  position  in  the 
same  du-ection.  The  distance  of  the  point  P  from  the 
middle  of  its  range,  0,  is  a  simple  harmonic  function 
of  the  time,  0  P  =y  =asm  {nt-\-e),  where  a  is  the  radius 
of  the  cii'cle — or  the  amplitude  of  the  simple  harmonic 
motion — e  is  the  angle  of  epoch,  and  n  is  the  angle  de- 
scribed by  the  moving  point  Q  in  the  unit  of  time.  The 
period  of  the  simple  harmonic  motion  is,  in  the  above 

27r      ,  .    nt  -\-  e 

case,  — .    Its  phase  is  —^ — . 

11  ^  27r 

Figure  2  presents  a  graph  of  simple  harmonic  mo- 
tion. As  in  Figure  1,  the  point  Q  moves  uniformly  in 
the  circle ;  the  point  P  performs  sunple  harmonic  motion 
according  to  the  formula  y=a  sin  {nt-\-e),  where  a  is 
the  amplitude  of  the  motion,  or  radius  of  the  circle,  e 
is  the  angle  of  the  epoch,  namely,  A  0  E,  and  n  is  the 
arc  described  by  Q  in  the  unit  of  time.    If  time  is  meas- 


10 


Economic  Cycles:  Their  Law  and  Cause 


ured  upon  the  line  B  C,  the  sinuous  curve  of  Figure  2 
is  the  graph  of  the  function,  y  ^asin  {nt-\-e). 


Figure  2. 

The  importance  of  simple  harmonic  functions  in 
the  study  of  periodic  phenomena  grows  out  of  the  fact 
that  any  periodic  curve  however  complex  ^  can  be  ex- 
pressed mathematically  by  a  series  of  simple  harmonic 
functions.  By  the  help  of  Fourier's  analysis  a  periodic 
function  may  be  put  in  the  form 

(1)  ?/  =^o  +  cti  COS  kt  +  tto  cos  2  H  +  as  cos  Zkt-k-  .  .  . 
+  6i  sin  ki  +  62  sin  2  kt  +  63  sin  3  A;i  +  .  .  . 

If  in  (1),  we  put, 

ai  =  Ai  sin  e^;  a^  =  A^  sin  e.,;  a^  =  A^  sin  e^',  &c., 
hi  =  Ay  cos  Ci;  62  =  ^2  cos  e,;  63  =  A3  cos  63;  &c., 

We  get, 

(2)  ?/  =  Ao  +Ai  sin  (/c/  +  ^i)  +  A.,  sin  (2  kt  +  63) 
4- A3  sin  (3A:^  +  e3)  +  .  .  . 

where  y  is  expressed  as  a  series  of  sines.    In  a  similar 

manner,  equation  (1)  may  be  expressed  as  a  series  of 

cosines, 

1  The  few  exceptions  to  the  general  rule  are  discussed  in  the 
mathematical  texts  that  develop  Fourier's  theorem. 


Cycles  of  Rainfall  1 1 

(3)  y  =  Ao  +  Bi  cos  (kt  -  c  i)  +  ^2  cos  (2  kt-e^) 

+  B^  cos  (3  A-f  -  e  3)  +  .  .   . 

In  the  use  of  Fourier's  theorem  for  the  purpose  of 
analyzmg  periodic  phenomena,  we  follow  a  process 
analogous  to  the  use  of  Taylor's  theorem  in  the  simpler 
demonstrations  of  mathematical  economics.  By  far 
the  greater  part  of  Cournot's  pioneer  treatise  and  of 
subsequent  work  of  his  school  is  based  upon  the  as- 
sumption that,  if  the  economic  function  under  investi- 
gation is  y=f{x),  then  fix +h)  may  be  expanded  by 
Taylor's  theorem,  and  the  first  terms  of  the  series  may 
be  used  as  an  approximation  to  the  form  of /(x).  Simi- 
larly, in  our  use  of  Fourier's  series,  the  attention  will  be 
focussed  upon  a  few  harmonics  as  a  first  approximation 
to  the  solution  of  the  problem  in  hand  of  expressing 
in  mathematical  form  the  periodicity  of  annual  rainfall. 

Assuming  that  any  periodic  function  may  be  ex- 
pressed as  a  Fourier  series,  the  problem  is  presented  of 
determining  the  values  of  the  coefficients.  The  series, 
as  we  know,  is  of  the  form 

y  =  / (0  =  Ao  +  Qi  COS  kt  +  a.2  COS  2  kt+  .  .  . 
+  bi  sin  kt  +  bo  sin  2  kt+   ... 

What  are  the  values  of  the  first  term  and  of  the  co- 
efficients of  the  sines  and  cosines?  In  order  to  deduce 
the  necessary  values,  we  shall  have  need  of  the  follow- 
ing lemma: 

If  7n  and  n  are  two  unequal  integers  and  k  is  put  equal 
to  -ji^,  then 


12  Economic  Cycles:  Their  Law  and  Cause 

I     cos  mkt  cos  nkt  di  =  0, 

/T 
sin  mkt  sin  nkt  dt  =  0, 

o 

/T 
sin  7/2.A-^  cos  nkt  dt   =0. 

o 

The  lemma  may  be  proved  to  be  true  by  evaluating  the 
three  integrals  according  to  the  usual  methods.  The 
first  integral,  for  example,  becomes 

COS  mkt  cos  nkt  dt  =  \    j  |  cos  (m—n)  kt +cos  (m+n)  kt\dt 

o  o 

rsin  (m-n)  kt      sin  (m  +  n)  ktV^ 
^  V  2  (m-w)  k    ^    2  {m  +  n)  k  L 

But  fc  =  -^,  and,  consequently,  I     cos  mkt  cos  nkt  dt  =  0. 

o 

With  the  aid  of  this  lemma  we  may  proceed  to  evalu- 
ate the  coefficients  in  Fourier's  series.  If  we  integrate 
the  series  between  the  Umits  o  and  T,  we  get, 

f  (t)  dt  =  A^    I    dt  +  Qi   j   COS  ktdt  +  bi  j    sin  kt  dt+  ..  . 

o  o  o  o 

But  all  of  the  terms  except  the  first  on  the  right-hand 
side  of  the  equation  will  vanish,  and  consequently 

/T 
/  (0  dt 

j''f{t)dt=  A,  j^dt  =  A,T, or  A,=  ^-^ 

o    *  o 

Since    /  f(i)dt  is  the  area  of  the  original  curve  for  one 

o 

whole  period  T,  the  constant  term  in  Fourier's  series  is 
equal  to  the  value  of  the  mean  ordinate  of  the  original 
curve. 


Cycles  of  Rainfall  13 

To  determine  the  value  of  Oi,  multiply  throughout 
by  cos  kt  and  integrate  between  Umits  o  and  T. 

/  {t)  COS  kt  dt  =  Ao   I    cos  kt  dt  +  a^  j    cos^  A;^  di 

o  o  o 

sin  A*^  cos  kt  dt  +  .  .  . 

o 

/  (0  COS  kt  dt  =  tti    I    C0S2  kt  dt,  since   /    cos  kt  dt  and 

o  o  o 

/T 
sin  A-<  cos  kt  dt  are  both  equal  to  zero  and  all  the  other 

o 

terms  on  the  right-hand  side  of  the  equation,  according 
to  our  lemma,  disappear.    But 


T''  ,.j.        pi  +  cos  2  A-^,^      ,   r,      sin2A-n^    T 

o  o 

and  as  a  result,  we  have  ^t 

/    /  (/)  cos  kt  dt 

fli  2  =   /    f  ^^^  ^^^  ^^  ^^'  or  Qj  =  2 ^ 

o 

Therefore  oi  is  equal  to  twice  the  mean  value  of  the 
product /(O  cos  kt. 

In  a  similar  manner  the  value  of  any  other  coefficient 
may  be  determined.  Take,  for  example,  b„.  Multiply 
throughout  by  sin  7ikt  and  integrate  between  o  and  T, 

n.  ,  .    ■       ,     ,       ,     H-        ,.j.      ,      r^  l-cos2nA;<  J, 
I  /  (0  sin  nkt  dt  =  bn   I   sm^  nkt  dt  =  b„  j    ^ ^^  = 

o  o  o 

,     f.r,     sin  2  nkiy  I  T 

/T 
.   Therefore  6„ 


14  Economic  Cycles:  Their  Law  and  Cause 

is   equal    to    twice   the    mean  value  of    the    product 
f{t)  sin  nkt. 

Having  found  the  algebraic  values  of  the  coefficients 
in  Fourier's  series,  we  may  now  proceed  to  determine 
their  statistical  equivalents  in  the  case  of  annual  rainfall. 

The  Periodograin  of  Rainfall 

If  the  length  of  a  cycle  of  rainfall  were  known  before- 
hand, the  preceding  exposition  of  Fourier's  theorem 
would  suffice  to  determine,  from  the  data  of  precipita- 
tion, the  amplitudes  and  phases  of  the  harmonic  con- 
stituents of  the  Fourier  series  descriptive  of  the  rainfall 
cycle.  But  in  the  problem  before  us  of  analyzing  the 
rainfall  data  of  the  Ohio  Valley,  we  do  not  know  whether 
there  are  many  cycles  or  only  one  cycle  or,  indeed, 
whether  there  are  any  cycles  at  all.  And  there  is  no 
short  method  of  solving  the  problem. 

Suppose,  for  example,  it  were  assumed  from  a  priori 
considerations  that  the  amount  of  rainfall  is  affected 
by  sunspots,  and,  as  sunspots  are  known  to  occur  in 
periods  of  about  eleven  years,  suppose  it  should  be  in- 
ferred that  the  annual  rainfall  will  likewise  show  a  period 
of  eleven  years.  If  the  rainfall  data  of  the  Ohio  Valley 
are  examined  for  an  eleven  years  period,  it  will  be  found 
that  the  data  yield  a  definite  amphtude  and  a  definite 
phase  for  a  cycle  of  eleven  years,  but  this  fact  is  no 
warrant  for  holding  that  there  is  a  true  rainfall  period  of 
eleven  years.  Every  other  grouping  of  the  seventy-two 
years  record  will  likewise  show  a  definite  amplitude 


Cycles  of  Rainfall  15 

and  a  definite  phase.  The  questions  that  one  is  in- 
terested to  have  answered  are:  (1)  What  is  the  law  of 
the  distribution  of  Fourier  coefficients  when  the  data 
are  analyzed  for  all  possible  periods;  and  (2)  how  may 
the  true  cycles  be  separated  from  the  accidental, 
spurious  cycles  that  are  obtained  when  the  data  are 
exhaustively  analyzed? 

In  Figure  3  the  results  of  a  detailed,  laborious  ex- 
amination of  the  data  of  annual  rainfall  in  the  Ohio 
Valley  are  presented  in  graphic  form.  On  the  axis  of 
abscissas  are  measured,  within  assigned  limits,  the 
possible  lengths  of  cycles  in  the  72  years  of  rainfall. 
By  extending  the  calculations  to  36  years,  we  obtain 
for  the  assumed  periods  a  record  of  possible  recur- 
rences varying  from  2,  in  case  of  the  period  of  36 
years,  to  24,  in  case  of  the  period  of  3  years.  On  the 
axis  of  ordinates  are  measured  the  squares  of  the  co- 
efficients of  the  first  harmonic  in  tlie  Fourier  series 
corresponding  to  the  lengths  of  periods  recorded  on 
the  axis  of  abscissas.  The  numerical  values  of  these 
squares  are  given  in  the  fourth  and  eighth  columns  of 
Table  II  in  the  Appendix  to  this  chapter.  The  method 
of  deriving  the  values  may  be  illustrated  by  taking  the 
cycle  of  8  years.  Suppose,  as  a  first  approximation, 
that  the  equation  to  Fourier's  series  is  put  in  the  alge- 
braic form 

y  =  F(t)  =  Ao  +  ai  cos  kt  +  bi  sin  kt'^=AQ+]Ai^sm(kt  +  e). 

Then  the  corresponding  arithmetical  values  derived 
from  the  Ohio  rainfall  data  are 


16 


Economic  Cycles:  Their  Law  and  Cause 


■//Pju/p^jo  satfoui  ui  3pn4iic/uje  at^j.  jo  a^enbc 


Cycles  of  Rainfall  17 

y  =  F{t)  =  41.19-3.13  cos  g-  ^  +  2.69  sin  -g-  i 

=  41.19+4.13  sin  (^  t  +  310°  41'). 

The  values  of  the  terms  a\,  6;,  A\  are  respectively 
(3.1339)-,  (2.6938)-,  (4.1325)-,  and  these  values  are 
given  in  the  proper  columns  of  Table  II  in  the  Ap- 
pendix. In  Figure  3,  the  values  of  A"^  for  the  several 
periods  are  measured  on  the  axis  of  ordinates. 

An  examination  of  Figure  3  will  illustrate  the  truth  of 
a  statement  advanced  a  moment  ago.  It  is  clear  from 
the  course  of  the  periodograph  ^  that  if  one  were  to 
take  any  period  at  random  between  the  hmits  of  3 
years  and  36  years,  he  would  in  every  case  obtain  a 
finite  value  for  the  amphtude  of  the  selected  cycle ;  and 
if,  by  chance,  selection  should  fall  upon,  say,  18,  or  21,  or 
29,  or  36  years,  an  argument  might  be  made  with  some 
degree  of  plausibility  that  a  real  cycle  had  been  dis- 
covered. But,  in  truth,  the  real  significance  of  no  one 
cycle  taken  at  random  can  be  judged  apart  from  its 
place  in  the  distribution  of  all  the  cycles  that  can  be 
derived  from  the  data. 

This  last  point  is  of  fundamental  importance.  The 
only  object  of  investigating  cycles  of  rainfall  or  cycles  of 
economic   phenomena   is   that   the   knowledge   of   the 

1  The  terms  periodograph  and  periodogram  were  coined  by  Pro- 
fessor Schuster. 

The  periodograph  is  the  cur\-e  tracing  the  values  of  A-;  the 
periodogram  is  the  surface  between  the  periodograph  and  tlie  base 
line  giving  the  lengths  of  the  periods.  Schuster:  "The  Period- 
ogram of  Magnetic  Declination,"  p.  108. 


18  Economic  Cycles:  Their  Law  and  Cause 

constant  recurrence  of  the  cycles  may  place  one  in  a 
position  to  foresee  and  utilize  the  dependent  phenomena. 
But  the  control  of  phenomena  dependent  upon  a  cycle 
presupposes  that  the  cycle  is  itself  a  real  phenomenon 
with  a  natural  cause,  and  that  consequently  it  persists 
with  an  increase  in  the  number  of  observations.  If, 
however,  an  apparent  cycle  of  any  length  taken  at 
random  is  obtained  from  the  given  data,  one  would 
surely  misspend  his  time  if  he  were  to  set  about  the 
search  for  its  cause,  and  were  to  derive  conclusions  based 
upon  the  hypothesis  of  the  persistence  of  the  cause. 
The  cycles  due  to  formal,  accidental  causes  must  be 
discriminated  from  the  cycles  with  natural  causes. 

The  separation  of  true  cycles  from  spurious  or 
accidental  cycles  is  facihtated  by  the  periodogram  ^  of 
observations.  If,  following  Professor  Schuster,  we  call 
the  square  of  the  amplitude  of  any  given  period  the 
"intensity"  of  the  period,  then  it  may  be  said  that  the 
probability  of  the  reality  of  a  period  is  dependent  upon 
the  ratio  of  its  intensity  to  the  mean  intensity  of  the 
periodogram.  Or,  again  following  Professor  Schuster, 
if  we  call  the  mean  intensity  of  the  periodogram  the 
''expectancy,"  then  the  reality  of  a  period  is  dependent 
upon  the  ratio  of  its  intensity  to  the  expectancy  of  the 
periodogram.  For  instance,  if  in  case  of  a  given  period 
the  ratio  of  intensity  to  expectancy  is,  say,  3  to  1,  then 
in  about  one  case  in  twenty  we  should  expect  to  obtain 
by  chance  a  greater  amphtude  than  the  amplitude  of 
the  particular  period  in  question.  If,  on  the  other  hand, 
1  See  the  preceding  note. 


Cycles  of  Rainfall  19 

the  ratio  were  say,  7  to  1,  a  greater  ratio  would  not 
occur  by  chance  once  in  a  thousand  times.  ^ 

With  these  facts  in  mind,  let  us  again  examine  Fig- 
ure 3.  It  is  clear  that  the  principal  periods  needing 
attention  are  those  respectively  of  8,  29,  33,  36  years. 
In  case  of  the  8  year  cycle  there  can  be  very  little 
doubt  as  to  the  existence  of  a  true  periodicity  approx- 
imating 8  years  in  length.  The  ratio  of  the  square  of 
its  amplitude  to  the  mean  square  amplitude  of  the 
periodogram  is  6.71  to  1.  We  may  accordingly  accept 
with  considerable  confidence  the  existence  of  a  natural 
period  of  rainfall  in  the  Ohio  Valley  approximating 
8  years  in  length. 

The  cycle  of  33  years,  inasmuch  as  the  ratio  of  the 
square  of  its  amplitude  to  the  mean  square  amplitude 
of  the  periodogram  is  3.27  to  1  is  in  all  probability  a 
true  cycle.  The  doubt  that  exists  is  due  to  the  smallness 
of  the  ratio  and  the   few   recurrences — only  two  -  — 

1  Schuster:  "The  Periodogram  of  Magnetic  Dechnation,"  pp.  124- 
125. 

2  Those  who  deprecate  the  use  of  such  meager  data  should  con- 
sider well  the  testimony  of  Lord  Kehdn  before  the  Meteorological 
Committee  of  the  Royal  Society,  1876. 

Question  1710.  "The  sum  which  parhament  will  give  for  this 
purpose  being  a  limited  sum,  do  you  think  that  it  would  be  well  to 
reduce  the  number  of  observations  in  order  to  have  more  money  to 
spend  upon  the  reduction  of  observations?  /  think  at  all  events  tintil 
one  eleven  yearn  period,  the  sun  spot  period,  is  completed,  it  would  be 
ivrong  to  reduce  the  number  of  observations." 

Question  1735.  "Supposing  that  you  had  one  of  these  analyses 
calculated  for  a  period  of  11  years,  would  each  year's  observations 
and  still  more  each  period  of  11  j^ears  observations,  require  to  be 
introduced  into  this  analysis  so  that  you  would  have  an  analysis  of 
22  years,  and  an  analysis  of  33  years,  and  so  on  from  time  to  time, 


20  Eco7iomic  Cycles:  Their  Law  and  Cause 

that  our  data  afford.  A  greater  confidence  in  the  exist- 
ence of  a  real  period  of  33  years  is  given  by  the  fact  that 
Briickner  ^  claims  to  have  found  a  true  period  of  about 
35  years  in  an  examination  of  a  vast  mass  of  rainfall 
material  all  over  the  world.  Accordingly,  the  existence 
in  the  Ohio  Valley  of  a  real  33  years  period  of  rainfall  we 
shall  assume  to  be  very  probable. 

The  other  two  periods  of  29  years  and  36  years  are 
not  easily  disposed  of.  But  in  the  first  place,  the  ratios 
of  the  squares  of  the  respective  amphtudes  to  the  mean 
square  amplitude  of  the  periodogram  are  not  such  as  to 
justify  the  acceptance,  with  any  degree  of  confidence,  of 
the  existence  of  true  cycles  of  29  years  and  36  years. 
In  the  second  place,  they  are  both  so  close  to  the  period 
of  33  years  as  to  cause  a  doubt  as  to  whether  they  may 
not  be  spurious  periods  that  are  likely  to  appear  in  the 
neighborhood  of  a  real  period.^ 

Considering  the  short  range  of  our  data  it  would  not 
be  properly  cautious  to  press  the  point  of  the  existence 
of  any  definite  real  cycle.  But  this  much  is  certain: 
If  there  are  true  cycles  in  the  data  of  the  72  years  of 
rainfall  in  the  Ohio  Valley,  there  is  far  greater  prob- 
abihty  that  two  cycles  are  those  of  8  years  and  33 
years  than  of  any  other  round  numbers  between  3  and 

or,  being  done,  would  it  be  done  once  for  all?  /  cannot  say  whether 
anything  with  reference  to  Terrestrial  Meteorology  is  done  once  for  all. 
I  think  probably  the  work  will  never  be  done." 

1  Edward  Bruckner:  Kliniaschwankungen  seit  1700.  Bruckner's 
period  fluctuates  greatly  in  length  and  has  an  average  value  of  35 
years. 

2  Schuster:  "The  Periodogram  of  Magnetic  Declination,"  p.  130. 


Cycles  of  Rainfall  21 

36  years.  Moreover,  the  periods  of  8  years  and  33 
years  afford  the  most  probable  basis  derivable  from  the 
data  upon  which  to  reason  both  as  to  the  future  course 
of  rainfall  in  the  Ohio  Valley  and  as  to  the  course  of  the 
phenomena  dependent  upon  rainfall. 

Assuming,  then,  that  for  the  purpose  in  hand,  the  33 
years  and  8  years  periods  are  the  most  probable  and 
valuable,  we  turn  to  the  consideration  of  the  equation 
to  the  graph  giving  the  course  of  rainfall  in  the  Ohio 
Valley. 

The  Equation  to  the  Rainfall  Curve 

It  will  be  helpful  to  approach  the  algebraic  descrip- 
tion of  the  cyclical  movement  of  rainfall  in  the  Ohio 
Valley,  by  observing  how  we  obtain  an  increasingly 
accurate  account  of  the  actual  rainfall  by  superposing 
the  constituent  cycles.  We  shall  use,  as  an  index  of  the 
relative  fit  of  the  several  curves,  the  root-mean-square 
deviation  of  the  observations  from  each  curve. 

If,  as  a  preliminary  step,  the  raw  data  of  the  course 
of  annual  rainfall  are  examined,  it  is  found  that  the 
mean  annual  rainfall  in  the  Ohio  Valley  is  41.19  inches, 
and  the  root-mean-square  deviation  about  the  mean  is 
/S  =  6.70  inches. 

If  the  long  33  years  cycle  is  considered  by  itself,  it 
appears  that  the  root-mean-square  deviation  about  the 
33  years  curve  is  >S  =  6.39  inches.  The  graph  of  the 
33  years  cycle  is  given  in  Figure  4.     Its  equation  is 

y  =  41.19  +  2.88  sin  (^  t  +  328°  7'V 


22  Economic  Cycles:  Their  Law  and  Cause 


Cycles  of  Rainfall  23 

the  origin  being  at  1839.  This  curve  traces  in  bold 
outline  the  general  course  of  ramfall.  It  gives  the 
ground-swell  of  the  rainfall  movement. 

If  the  8  years  cycle  is  superposed  upon  the  33  years 
cycle,  the  root-mean-square  deviation  about  the  curve 
becomes  S  =  5.66  inches.  The  graph  of  the  combination 
of  these  two  curves  is  traced  in  Figure  5.    Its  equation  is 

1/  =  41.19 +  2.88 sin  (1^^  +  328°  7') +4.13  sin  (I'i  +  SIOMI'), 

the  origin  being  at  1839.  A  point  of  interest  with  regard 
to  the  flow  of  the  curve  is  the  rapidity  with  which  it 
rises  from  the  least  minimum  to  the  greatest  maximum, 
and  the  slowness  with  which  it  then  descends  to  the 
subsequent  least  minimum. 

If  the  8  years  cycle  and  its  semiharmonic  of  4  years 
are  combined  with  the  33  years  cycle  and  its  semi- 
harmonic  of  16.5  years,  the  root-mean-square  deviation 
about  the  compound  curve  becomes  *S=5.29  inches. 
The  graph  of  the  curve  is  given  in  Figure  6.  Its  equa- 
tion is 

7/ =4 1.19  +  2.88  sin (1^  i  +  328°  7')  +  2.25  sin  (';*^^ +  27 P  42') 

+  4.13  sin/^  t+3l0°  41')  +  2.14  sin/^  t  +  180°  28') , 

the  origin  being  at  1839.  In  this  closer  approximation 
the  characteristic  rapid  rise  to  a  general  maximum  and 
slow  fall  to  a  general  minimum  is  reproduced.  Another 
characteristic  is  the   longer  interval  that   the   curve 


24 


Economic  Cycles:  Their  Law  and  Cause 


siL/ou:  ui  iiejuipj  /enuu\/ 


Cycles  of  Rainfall 


25 


tiL/iui  ui  ijefuipj  ienuu\/ 


26  Economic  Cycles:  Their  Law  and  Cause 

lingers  at  the  minima  and  the  short  period  during  which 
it  flows  in  the  neighborhood  of  the  maxima.^ 

Rainfall  in  the  Corn  Belt 
Thus  far  we  have  dealt  with  the  law  of  rainfall  only 
in  the  Ohio  Valley.  The  object  in  taking  the  Ohio 
data,  rather  than  the  data  of  a  state  more  representa- 
tive of  the  leading  cereal  area,  was  to  make  an  investiga- 
tion of  a  longer  meteorological  record  than  is  afforded 
by  the  data  of  the  central  Mississippi  Valley.  But  our 
purpose  in  dealing  with  meteorological  records  at  all  is 
to  show  the  dependence  of  crops  upon  the  cyclical 
movement  of  the  elements  of  the  weather.  We  must, 
therefore,  prove  that  the  cycles  of  rainfall  which  we  have 

1 1  should  like  to  make  clear  the  method  I  have  followed  in  the 
derivation  of  the  equations  to  the  cun'es.  My  object  was  to  obtain 
a  summaiy  description  of  the  general  course  of  rainfall  in  order  that 
I  might  discover,  later  on,  whether  the  characteristic  general  fea- 
tures of  the  movement  of  rainfall  are  reproduced  in  the  changing 
yield  per  acre  of  the  crops.  As  a  first  step  I  tried  to  detect  the  real 
cycles  in  rainfall  and  I  believe  I  have  sho^\^l  that,  if  the  72  years 
record  is  sufficiently  long  to  reveal  the  true  cycles,  then  the  most 
probable  lengths  of  the  cycles  are,  in  round  numbers,  33  years  and 
8  years  respectively.  With  so  short  a  range  of  data  I  regarded  it  as 
useless  to  attempt  to  calculate  the  lengtlis  of  the  periods  to  a  greater 
degree  of  precision.  I  next  had  to  derive  the  equations  to  the  curves 
showing  the  characteristic  general  course  of  rainfall,  and  it  seemed 
to  me  that,  for  this  purpose,  the  method  described  in  the  text  for 
evaluating  the  coefficients  in  a  Fourier  series  might  properly  be 
used.  If  the  33  years  cycle  were  taken  as  the  fundamental  cycle, 
then  the  8  years  cycle  would  be  approximately  the  fourth  harmonic 
in  the  series,  and  the  4  j^ears  cycle  would  be  the  eighth  harmonic. 

The  arithmetical  process  for  computing  the  coefficients  is  indi- 
cated by  Professor  Schuster  in  Hidden  Periodicities,  pp.  13,  14  and  is 
briefly  described  by  Professor  Perry  in  an  article  on  "Harmonic 
Analysis"  in  The  Electrician,  for  February  5,  1892. 


Cycles  of  Rainfall  27 

discovered  for  the  Ohio  Valley  are  likewise  the  cycles 
that  exist  in  the  heart  of  the  grain  producing  area. 

.■Vmong  the  states  of  the  Middle  West,  Illinois  is 
probably  the  most  highly  representative  of  American 
cereal  production.  It  produces  the  largest  crop  of 
corn/  which  is  the  leading  American  cereal,  and  it 
ranks  second  in  the  production  of  oats.  Most  of  the 
other  cereals  that  are  produced  in  the  upper  Mississippi 
Valley  are  likewise  cultivated  with  success  in  Illinois. 
Another  fact  that  makes  Illinois  a  desirable  state  for 
our  purpose  is  that  its  meteorological  records  are  fairly 
long  and  are  obtainable  from  so  many  stations  as  to  be 
representative  of  the  weather  conditions  in  the  entire 
state.  This  last  fact  is  all-important  if  the  statistics 
for  crop  production  of  the  whole  state  are  to  be  con- 
sidered in  relation  to  the  weather  cycles  of  the  state. 

In  Table  III  of  the  Appendix  to  this  chapter  the 
record  of  the  annual  rainfall  in  Illinois  is  given  for  a 
period  of  41   years.'-     The  ideal  direct  method  with 

1  This  statement  was  accurate  when  it  was  first  \\Titten.  But  in 
1912  Iowa  gained  by  a  narrow  margin  the  first  place  among  the  corn 
producing  states. 

2  The  raw  data  were  taken  from  Bulletin  W  of  the  Weather  Bu- 
reau of  the  United  States  and  from  the  Annual  Reports  of  the  Chief 
of  the  Weather  Bureau.  The  stations  used  in  computing  the  mean 
annual  rainfall  were: — In  Northern  lUinois:  Aurora,  Cambridge, 
Chicago,  Tiskilwa,  Galva,  Kishwaukee,  Ottawa,  Winnebago,  and 
Henry.  In  Central  Illinois:  Charleston,  Carlinville,  Coatsburg, 
Decatur,  Griggsville,  Knoxville,  Havana,  LaHarpe,  Pana,  Peoria, 
and  8j)ringfield.  In  Southern  Illinois:  Cairo,  Cobden,  Carlyle, 
Golconda,  Flora,  Greenville,  McLeansboro,  Mascoutah,  Mt. 
Carmcl,  and  Palestine. 

All  of  these  stations  do  not  present  full  records  for  the  41  years. 


28  Economic  Cycles:  Their  Law  and  Cause 

reference  to  these  data  would  be  to  compute  the 
periodogram  in  the  same  manner  in  which  it  was  com- 
puted in  the  case  of  the  Ohio  Valley  data,  and  then  com- 
pare the  periodograms.  But  this  method  has  not  been 
followed.  A  less  direct,  and  far  less  laborious,  process 
has  been  adopted.  We  know  from  the  Ohio  data  that 
there  are  two  cycles  of  rainfall,  a  33  years  cycle  and  an  8 
years  cycle,  and  we  know,  furthermore,  that  when  the 
curve  for  rainfall  in  the  Ohio  Valley  is  computed  for  the 
33  years  and  8  years  periods  and  their  semiharmonics,  a 
good  fit  to  the  data  is  obtained.  The  questions  that  are 
asked  with  reference  to  the  Illinois  data  are  these: 
If  we  assume  the  existence  of  a  33  years  period  and  an 
8  years  period  in  the  Illinois  rainfall  data,  will  the 
rainfall  curve  fit  the  Illinois  data  as  well  as  the  Ohio 
curve  fits  the  Ohio  data?  Will  the  Illinois  curve  re- 
produce the  characteristic  features  of  the  Ohio  curve? 
A  presumption  in  favor  of  an  affirmative  answer  to 
these  questions  is  suggested  by  the  fact  that  the  correla- 
tion between  the  annual  rainfall  in  the  Ohio  Valley  and 
the  annual  rainfall  in  the  state  of  Illinois  is  r=6.00. 
The  graph  of  the  curve  of  rainfall  in  Illinois  is  given 
in  Figure  7.    Its  equation  is 

2/ =38.53 +3.03  sin  /||  ^+325°  35'^  +  1.87  sin  (^^  ^+ 194°  55') 

+3.05  sin  (^  ^ +241°  52')  +  1 .  12  sin  /^  f +232°  26') , 

the  origin  being  at  1870.    The  root-mean-square  devia- 

but  in  no  year  were  fewer  than  seven  records  obtainable  while  for  a 
large  proportion  of  the  years  the  thirty  records  were  complete. 


Cycles  of  Rainfall 


29 


+ 


+ 


+ 


a] 

194° 
rigin 

+   o 

t>- 

■^  1  CO 

+ 


sai^oui  ui  iiBj-UiPJ  jDnuuY 


30  Economic  Cycles:  Their  Lmv  and  Cause 

tion  of  the  observations  from  this  curve  is  S  =4.20.  In 
case  of  the  Ohio  curve  the  root-mean-square  deviation 
was  5=5.29.  But  this  is  a  better  relative  fit  for  the 
lUinois  curve  than  we  have  a  right  to  claim,  because  in 
Ohio  the  mean  annual  rainfall  is  41.19,  while  in  Illinois 
the  mean  is  38.53.  If  we  express  the  relative  scatter  of 
the  observations  about  the  curve  as  the  ratio  of  the 
root-mean-square  deviation  of  the  observations  to  the 
mean  rainfall,  we  get  for  Ohio  and  Illinois,  respectively, 
5^  =  . 128;. SI  =  .109. 

In  Figure  8,  the  Ohio  curve  for  1870-1910  is  placed 
upon  the  same  chart  as  the  Illinois  curve  for  the  same 
flow  of  time,  and  the  degree  of  correspondence  of  the 
two  curves  is  seen  to  be  so  close  that,  with  due  allowance 
for  the  difference  in  their  mean  annual  rainfall,  they 
seem  to  be  almost  congruent. 

We  may  say,  therefore,  that  the  two  curves  fit  their 
respective  data  equally  well. 

Our  problem  has  now  received  its  solution.  Annual 
rainfall  in  the  chief  grain-producing  area  of  the  United 
States  has  no  secular  trend,  but  its  mean  course  is  the 
resultant  of  causes  producing  two  cycles  of  33  years 
and  8  years  respectively.  The  manner  in  which  these 
cycles  of  rainfall  produce  a  rhythmical  expansion  and 
contraction  in  the  yield  of  the  crops  we  shall  examine  in 
the  next  chapter. 


Cycles  of  Rainfall 


31 


Tai^Dui  ui  IIPJ.UIPJ  jpnuu^ 


32 


Economic  Cycles:  Their  Law  and  Cause 


APPENDIX 


TABLE  I. — Annual  Rainfall  in  the  Ohio  Valley 
Stations:  Cincinnati,  Portsmouth,  Marietta 


Year 

Rainfall  in  \ 
Inches 

Year 

Rainfall  in 
Inches 

Year 

Rainf.vll  in 
Inches 

1839 

29.92 

1863 

37.95 

1887 

38.00 

1840 

42.84 

1864 

36.68 

1888 

46.19 

1841 

43.94 

1865 

48.93 

1889 

37.06 

1842 

41.89 

1866 

47.37 

1890 

55.43 

1843 

48.20 

1867 

40.72 

1891 

40.68 

1844 

37.95 

1868 

46.87 

1892 

36.96 

1845 

40.11 

1869 

41.29 

1893 

40.80 

1846 

48.39 

1870 

37.46 

1894 

31.07 

1847 

55.26 

1871 

29.91 

1895 

29.05 

1848 

44.97 

1872 

32.90 

1896 

39.22 

1849 

46.37 

1873 

45.18 

1897 

44.80 

1850 

54.77 

1874 

38.48 

1898 

45.04 

1851 

32.54 

1875 

44.78 

1899 

40.46 

1852 

46.73 

1876 

47.34 

1900 

*  33.60 

1853 

35.67 

1877 

34.69 

1901 

31.78 

1854 

40.30 

1878 

36.35 

1902 

39.53 

1855 

47.89 

1879 

39.22 

1903 

37.98 

1856 

28.98 

1880 

49.94 

1904 

28.24 

1857 

37.95 

1881 

41.60 

1905 

42.81 

1858 

55.48 

1882 

56.10 

1906 

41.95 

1859 

46.68 

1883 

49.25 

1907 

46.68 

1860 

36.00 

1884 

40.05 

1908 

33.29 

1861 

43.81 

1885 

37.63 

1909 

41.40 

1862 

40.26 

1886 

39.61 

1910 

36.20 

Cycles  of  Rainfall 


33 


TABLE  II. — The    Periodogram    of    Rainfall   in   the    Ohio 

Valley 

y  =  F(t)  =  Ao  +  ai  cos  kt  +  bi  sin  kt  =  Ao  -{-  Ay  sin  (kt  -f-  e) 


Length 

OF 

Period 

IN  Years 

o- 

6^ 

a2+62=A2 

Length 
OF  Pe- 
riod IN 
Years 

a2 

6- 

a^+b-=A- 

3 

1.2628 

2.4821 

3.7449 

21 

.0046 

4.4260 

4.4306 

4 

.0003 

4.5689 

4.5692 

22 

.2454 

2 . 4237 

2.6691 

5 

.0897 

.4520 

.5417 

23 

.8471 

.8714 

1.7185 

6 

.2220 

.  1403 

.3623 

24 

.3551 

.0678 

.4229 

7 

2.1838 

3.7869 

5.9707 

25 

.2755 

.  1327 

.4082 

8 

9.8215 

7.2563 

17.0778 

26 

.0566 

.0002 

.0568 

9 

.0327 

.3120 

.3447 

27 

.9692 

.0019 

.9711 

10 

.5978 

.0190 

.6168 

28 

.6227 

.0300 

.6527 

11 

1.0756 

.6791 

1.7547 

29 

4.2657 

1.1153 

5.3S10 

12 

.4371 

.1143 

.5514 

30 

.6464 

.4767 

1 . 1231 

13 

.0044 

.0007 

.0051 

31 

.6112 

.5923 

1.2035 

14 

.1078 

.1670 

.2748 

32 

.5776 

1.1168 

1.6944 

15 

.  1874 

.0863 

.2737 

33 

2.3199 

5.9974 

8.3173 

16 

.7691 

.0424 

.8115 

34 

.2017 

1.76.52 

1.9669 

17 

.9795 

.0626 

1.0421 

35 

.0456 

1.7914 

1.8370 

18 

2.9332 

.9270 

3.8602 

36 

.0036 

6.8567 

6.8603 

19 
20 

1.4777 
.0294 

1 . 9422 
1.5961 

3.4199 
1.6255 

Mea 

n  value 

of  A'  =  2.5459 

34 


Economic  Cycles:  Their  Law  and  Cause 


TABLE  III. — Annual  Rainfall  in  Illinois 


Year 

Rainfall  in  Inches 

Year 

Rainfall  in  Inches 

1870 

29.65 

1891 

34.11 

1871 

36.53 

1892 

44.17 

1872 

33.98 

1893 

35.89 

1873 

41.62 

1894 

28.99 

1874 

32.91 

1895 

32.92 

1875 

40.34 

1896 

38.27 

1876 

45.50 

1897 

37.44 

1877 

42.76 

1898 

49.09 

1878 

37.61 

1899 

34.95 

1879 

36.10 

1900 

36.19 

1880 

42.31 

1901 

27.17 

1881 

42.32 

1902 

42 .  65 

1882 

49.04 

1903 

35.97 

1883 

47.81 

1904 

39.33 

1884 

45.83 

1905 

37.33 

1885 

40.80 

1906 

38.10 

1886 

36.16 

1907 

40.61 

1887 

33.40 

1908 

36 .  76 

1888 

39.41 

1909 

44.74 

1889 

36.27 

1910 

34.34 

1890 

40.34 

Mean 

38.53 

CHAPTER   III 

RAINFALL  AND  THE   CROPS 

"It  is  mere  weather  .  .  .  doing  and  undoing  without  end." 

— William  James. 

In  the  preceding  chapter  the  course  of  annual  rainfall 
in  the  great  cereal-producing  area  of  the  United  States 
has  been  shown  to  move  in  cycles:  There  is  a  ground- 
swell  of  thirty-three  years  in  length  upon  which  cycles 
of  eight  years  in  duration  are  superposed.  Our  object 
in  studying  the  rhythmic  changes  in  the  volume  of  rain- 
fall was  to  bring  these  changes  into  relation  with  the 
variations  in  the  yield  per  acre  of  the  crops,  and  in  the 
present  chapter  we  shall  be  able  to  i-ealize  our  purpose. 
The  actual  course  of  the  varying  yield  per  acre  of  the 
crops  will  be  shown  to  have  both  a  secular  and  a  cyclical 
movement;  these  two  movements  will  be  separated  for 
representative  crops;  and  the  cyclical  movements  will 
be  shown  to  be  dependent  upon  the  cyclical  movements 
in  the  weather  represented  by  the  cycles  of  rainfall. 

The  Secular  Trend  in  the  Yield  of  the  Crops 

The  state  of  Illinois  was  chosen  in  the  preceding 
chapter  to  illustrate  the  general  conditions  of  rainfall 
in  the  Corn  Belt  of  the  Middle  West,  and  we  shall  now 
examine  the  statistics  of  the  yield  of  its  most  important 
crops. 

35 


Acreage 

Value  of  Crop 

10,658,000 

$174,791,000 

4,220,000 

54,818,000 

2,512,000 

41,152,000 

1,183,000 

8,641,000 

137,000 

8,302,000 

57,000 

952,000 

48,000 

538,000 

4,000 

70,000 

900 

62,000 

36  Economic  Cycles:  Their  Law  and  Cause 

According  to  the  Yearbook  of  the  Department  of 
Agriculture  for  1912,  we  find  the  acreage  and  value  of 
the  leading  Illinois  crops  as  they  are  given  in  the 
subjoined  Table: 

Acreage  and  Value  of  Crops  in  Illinois,  1912 

Crop 

(1)  Corn 

(2)  Oats 

(3)  Hay 

(4)  Wheat 

(5)  Potatoes 

(6)  Barley 

(7)  Rye 

(8)  Buckwheat 

(9)  Tobacco 

It  is  clear,  from  this  Table,  that  five  crops — corn,  oats, 
hay,  wheat,  and  potatoes — make  up  the  bulk  of  the 
crops  of  lUinois,  and  one  could  not  go  far  wrong  if  he 
based  his  generalizations  as  to  the  conditions  of  agricul- 
ture in  the  state  upon  these  five  crops.  But  for  the 
purposes  we  have  in  view,  in  this  and  other  chapters,  it 
is  not  possible  to  utilize  the  statistics  of  wheat  produc- 
tion because  both  spring  and  winter  wheat  are  grown  in 
the  state,  and  the  statistics  of  their  relative  yield  and 
price  are  not  given  in  the  published  material  for  the 
long  record  covered  in  our  investigation.  Accordingly, 
the  crops  that  have  been  actually  used  in  our  inquiry 
are  corn,  oats,  hay,  and  potatoes.  These  crops  total 
93.13  per  cent,  of  the  crop  acreage  and  96.45  per  cent,  of 
the  crop  value  as  these  quantities  are  given  in  the'above 
Table. 


Rainfall  and  the  Crops  37 

As  the  yield  per  acre  of  the  various  crops  may  show  a 
secular  as  well  as  a  complex  cyclical  change,  it  will  be 
necessary,  before  their  cyclical  elements  can  be  brought 
into  relation  with  the  corresponding  cyclical  changes  of 
rainfall,  to  eliminate  from  the  recorded  course  of  the 
yield  per  acre  of  the  several  crops  the  element  of  change 
that  is  secular  in  character. 

The  method  that  has  been  adopted  here  to  effect  the 
elimination  of  the  secular  change  is  simple,  but  to  secure 
a  first  approximation,  it  is  adequate.  For  a  period  of 
time  covered  by  the  statistics,  a  change  is  regarded  as  a 
secular  change  if,  for  the  period  of  time  taken  as  a 
whole,  the  yield  per  acre  of  the  crop  shows  a  tendency 
either  to  increase  or  to  decrease.  In  order  to  determine 
whether  there  is  a  secular  change  in  the  yield  per  acre, 
for  a  certain  period  of  time,  the  yield  data  are  correlated 
with  time,  and  the  existence  or  non-existence  of  a 
secular  change  is  inferred  from  the  relative  magnitudes 
of  the  coefficient  of  correlation  and  its  probable  error. 
If  there  be  a  secular  change,  the  calculation  of  the 
coefficient  of  correlation  of  the  yield  with  time  is  then  a 
first-step  toward  the  elimination  of  the  secular  element 
by  means  of  a  regression  equation  in  which  the  co- 
efficient of  correlation  is  a  factor. 

The  method  may  be  illustrated  by  taking  the  history 
of  the  yield  per  acre  of  corn.  In  Figure  9  the  actual 
yield  per  acre  in  Illinois  is  plotted  for  the  period  1870- 
1910.  The  straight  fine  showing  the  secular  trend  of  the 
yield  is  the  graph  of  the  regression  equation  between 
the  yield  per  acre  and  time.     The  correlation  of  the 


38  Economic  Cycles:  Their  Law  and  Cause 


3JOQ  j^cf  u^ooj.o  sf9i^sng 


Rainfall  and  the  Crops  39 

yield  per  acre  and  time  is  r  =  .382  ±  .090,  and  the  regres- 
sion equation  is,  ?/ =  .204x +26.93,  where  y=  yield  per 
acre,  a:  =  time,  and  the  origin  is  at  1870.  The  secular 
trend  is  eliminated  by  means  of  the  facts  summarized 
in  the  regression  equation:  Beginning  with  the  year 
1870,  as  many  times  .204  are  subtracted  from  the 
jdeld  per  acre  for  the  several  years,  as  the  respective 
years  differ  from  1870.  For  example,  the  yield  for  the 
year  1872  was  39.8  bushels  per  acre;  consequently  the 
reduced  yield  for  that  year  was  39.8-2(.204)  =39.8- 
.408  =39.39.  Figure  10  traces  the  yield  per  acre  of  corn 
freed  from  the  secular  trend. 

Of  the  four  leading  crops  of  Illinois  that  form  the 
basis  of  our  investigation,  only  two,  corn  and  potatoes, 
show  a  significant  ^  tendency  to  secular  change.  The 
correlation  between  the  yield  per  acre  and  time  is, 
for  hay,  r  =  .013 ±.105  and,  for  oats,  r  =  .043 ±.105; 
consequently  the  figures  for  the  yield  per  acre  of  these 
two  crops  have  not  been  reduced.  In  the  case  of 
potatoes,  r  =  .122 ±.104,  and  the  regression  equation 
is  1/  =  .233^+70.51,  where  the  origin  is  at  1870.  The 
figures  for  the  actual  yield  per  acre  and  the  reduced 
yield  per  acre  for  corn  and  potatoes,  as  well  as  the 
figures  for  the  yield  of  hay  and  of  oats,  are  given  -  in 
Table  I  of  the  Appendix  to  this  chapter. 

1  The  indicated  secular  trend  in  potatoes  is  not  significant  in 
the  mathematical  sense,  because  the  probable  error  of  the  coefficient 
of  correlation  is  nearly  as  large  as  the  coefficient  itself.  I  have 
nevertheless  eliminated  the  indicated  secular  trend  before  using  the 
data. 

2  The  raw  data  were  taken  from  BuUelins  56,  58,  62,  63  of  the 


40 


Economic  Cycles:  Their  Law  and  Cause 


1                                                1                                               1                                               1                                               1 

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Rainfall  and  the  Crops  41 

Critical  Periods  Of  Growth 

If  the  rhythmical  changes  in  rainfall  are  to  give  the 
clue  to  the  changes  in  the  yield  of  the  crops,  the  varia- 
tions in  the  rainfall  must  be  closely  related  with  the 
variations  in  the  yield  of  the  crops.  But  different  crops 
have  different  times  of  planting  and  of  harvesting, 
different  periods  of  growth,  and  different  requirements 
of  moisture  at  the  various  stages  of  growth.  The  direct 
Way  to  find  whether  the  course  of  rainfall  determines 
the  course  of  the  varying  yield  of  the  crops  is  first  to 
ascertain  the  critical  season  for  every  crop ;  and  then  to 
compare  the  course  of  the  yield  of  each  crop  with  the 
course  of  the  rainfall  of  its  critical  season. 

The  method  of  discovering  the  critical  period  of  a. 
crop  may  be  illustrated  in  the  treatment  of  corn.  In 
Table  II  of  the  Appendix  to  this  chapter,  the  mean  ^ 
monthly  rainfall  for  Illinois  is  tabulated  for  seven 
months,  March,  April,  May,  June,  July,  August,  and 
September.    Table  I  of  the  Appendix  records  the  data 

Bureau  of  Statistics  of  tlie  United  States  Department  of  Agriculture 
and  from  recent  Yearbooks  of  the  United  States  Department  of 
Agriculture. 

1  The  raw  data  were  taken  froni  Bulletin  W  of  the  Weather 
Bureau  of  the  United  States  and  from  the  Annual  Reports  of  the 
Chief  of  the  Weather  Bureau.  The  stations  used  in  computing  the 
mean  monthly  rainfall  were,  in  Northern  Illinois:  Aurora,  Cam- 
bridge, Chicago,  Tiskilwa,  Galva,  Kishwaukee,  Ottawa,  Winnebago 
and  Henry.  In  Central  Illinois:  Charleston,  Carlinville,  Coatsburg, 
Decatur,  Griggsville,  Knoxville,  Havana,  LaHar])e,  Pana,  Peoria 
and  S])ringfield.  In  Southern  Illinois:  Cairo,  Cobden,  Carlyle, 
Golconda,  Flora,  Greenville,  McLeansboro,  JMascoutah,  Mt. 
Carmel  and  Palestine. 


42  Economic  Cycles:  Their  Law  and  Cause 

referring  to  the  yield  per  acre  of  the  several  crops  after 
the  secular  trends  have  been  eliminated.  These  two 
Tables  furnish  the  statistical  material  for  ascertaining 
the  critical  periods  of  the  respective  crops.  The  facts 
as  to  the  times  of  planting  and  harvesting  may  be 
obtained  from  an  article  in  the  Yearbook  of  the  United 
States  Department  of  Agriculture,  1910,  pp.  488-494, 
on  ''Seedtime  and  Harvest:  Average  Dates  of  Planting 
and  Harvesting  in  the  United  States."  The  method  of 
detecting  the  period  of  critical  relation  between  yield 
and  rainfall  consists  in  ascertaining,  for  each  crop,  the 
month  or  combination  of  months,  within  the  interval 
between  planting  and  harvesting,^  whose  rainfall  gives 
the  highest  correlation  with  the  ultimate  yield  per 
acre  of  the  crop.  The  time  for  planting  corn  in  Ilhnois, 
according  to  the  official  publication  cited  above,  begins 
about  April  30,  it  is  general  about  May  13,  and  it  ends 
about  June  2.  The  average  time  for  harvesting,  accord- 
ing to  the  same  publication,  begins  about  September  26, 
is  general  by  October  29,  and  ends  about  December  10. 
The  correlation  between  the  yield  of  corn  per  acre 
(secular  trend  eliminated),  and  the  rainfall  for  June  is, 
r  =  .069;  for  July,  r  =  .496;  for  August,  r  =  .293;  for 
September,  r  =  .087 ;  for  July  and  August  combined, 
r  =  .589.  The  critical  period  of  growth  for  corn  has, 
therefore,  been  assumed  to  be  the  interval  of  two 
months — July  and  August.^ 

1  For  some  purposes  it  would  be  desirable  to  test  the  correlation 
beyond  these  limits. 

2  Of  course  all  possible  combinations  of  months  have  not  been 


Rainfall  and  the  Crops  43 

The  critical  periods  for  the  other  crops  are,  for  oats — 
May,  June,  July,  r  =  .290;  for  hay — March,  April, 
May,  June,  r  =  .620;  for  potatoes — July  and  August, 
r  =  .666.  The  critical  season  for  corn,  as  we  found  a 
while  ago,  is  July  and  August,  r  =  .589. 

The  high  correlation  between  the  yield  of  the  crops 
and  the  rainfall  of  their  respective  critical  seasons 
promises  well  for  the  theory  as  to  the  relation  of  the 
cycles  of  rainfall  and  cycles  of  crops.  In  the  last  chapter 
we  found  that  by  examining  the  periodogram  of  annual 
rainfall  in  the  Ohio  Valley,  cycles  of  eight  years  and  of 
thirty-three  years  were  discovered;  and  that  by  taking 
periods  of  thirty-three  years  and  eight  years  with  their 
semiharmonics,  a  good  fit  to  the  annual  rainfall  curve 
was  obtained.  It  was  then  shown  that  the  annual  rain- 
fall in  Illinois  is  correlated  with  the  annual  rainfall 
in  the  Ohio  Valley,  the  correlation  coefficient  being 
r  -  .600.  Upon  the  basis  of  this  relatively  high  correla- 
tion, it  was  assumed  that  the  annual  rainfall  in  Ilhnois 
passed  through  similar  cycles  to  the  rainfall  in  the 
Ohio  Valley,  and  we  found  that  this  assumption  was 
justified  by  the  facts  inasmuch  as  the  harmonic  analysis 
applied  in  the  same  way  to  the  Ilhnois  data  afforded  as 
good  a  fit  as  when  it  was  apphed  to  the  data  of  the 
Ohio  Valley.  Since  in  two  of  the  four  representative 
crops  the  correlation  between  the  yield  and  the  rainfall 

exhausted  in  the  above  case,  nor  have  we  made  any  attempt  to 
place  the  critical  period  for  a  smaller  interval  of  time  than  a  month. 
If  for  any  other  period  a  closer  relation  could  be  found  than  r  =  .589, 
the  conclusions  that  we  draw  from  our  investigation  would  only  be 
strengthened. 


44  Economic  Cycles:  Their  Law  and  Cause 

of  the  critical  season  of  growth  is  greater  than  the 
correlation  between  the  annual  rainfall  in  Illinois  and 
the  annual  rainfall  in  the  Ohio  Valley,  there  would 
seem  to  be  excellent  ground  for  beheving  that  the  cycles 
of  the  yield  of  the  crops  would  flow  congruently  with 
the  cycles  of  rainfall  during  their  respective  critical 
periods. 

Cycles  in  the  Yield  of  the  Representative  Crops  and  the 
Corresponding  Cycles  of  Rainfall 

The  method  of  bringing  the  cycles  of  rainfall  for  the 
critical  period  of  growth  of  the  several  crops  into  rela- 
tion with  the  cycles  of  the  respective  crops  is  similar  to 
the  method  that  was  employed  in  passing  from  the 
cycles  of  annual  rainfall  in  the  Ohio  Valley  to  the 
corresponding  cycles  in  the  state  of  IlUnois.  The 
laborious  but  direct  way  of  treating  the  problem  would 
be  to  compute  the  periodogram  of  rainfall  for  the 
critical  period  of  growth  of  each  crop,  and  then  to  com- 
pare the  results  with  the  corresponding  periodograms  of 
the  respective  crops.  It  may  be  that  this  laborious 
process  may  eventually  have  to  be  followed.  The 
process  that  has  been  adopted  in  the  present  investiga- 
tion makes  several  assumptions  which  it  is  highly 
desirable  to  have  clear  in  mind.    It  is  assumed 

(1)  That  the  course  of  the  annual  rainfall  is  the  mean 

course  of  the  rainfall  of  the  parts  of  the  year 

and   that,    consequently,   by   computing   the 

:    :         periodogram  of  annual  rainfall,  we  obtain  a 

general  type  of  curve  for  describing  not  only 


Rainfall  and  the  Crops  45 

the  annual  rainfall  but  also  the  rainfall  of 
any  considerable  part  of  the  year.  Or,  more 
concretely,  that  the  annual  rainfall  and  the 
rainfall  of  any  considerable  part  of  the  year 
may  be  described  by  an  equation  of  the  form 


+  «i  sin  l-^t  +  rjA  +  a^^  sin  (^y  ^  +  ■»?•.) , 


where  the  constants  in  the  series  may  be  differ- 
ent for  the  several  parts  of  the  year, 

(2)  That  where  the  correlation  between  the  yield  per 

acre  of  a  particular  crop  and  the  rainfall  of  its 
critical  season  is  high,  the  same  general  type 
of  equation  will  fit  both  groups  of  data,  the 
data  of  rainfall  and  the  data  of  the  yield  per 
acre  of  the  crops. 

(3)  That   both   of   the   i^receding   assumptions   are 

greatly  fortified  if  the  compound  curves  de- 
duced from  the  actual  data  of  rainfall  and 
yield  satisfy  a  reasonable  test  of  fit  to  the  data. 

The  working  out  of  the  consequences  of  these  as- 
sumptions is  exliibited  in  Figures  11,  12,  13,  and  the 
equations  descriptive  of  the  several  curves  appear  on 
the  corresponding  Figures. 

To  measure  the  degree  of  fit  of  the  curves  to  their 
respective  data,  we  shall  employ  a  coefficient  K,  which 
may  be  described  as  the  ratio  of  the  arithmetical  sum 
of  the  deviations  of  the  observations  from  the  curve 


46 


Economic  Cycles:  Their  Law  and  Cause 


Bushels    o-f pofafoes  per  acre 


'^FO^ny  pup  ^/"P  'sSLjOui  ui  npjuie^ 


Rainfall  and  the  Crops 


47 


Tons  of  hdy  per  acre 


■9unp'/p(^'ludY'LiDjei^'saLfOui  ui  //P/i^'Py 


48 


Economic  Cycles:  Their  Law  and  Cause 


Bushels   of  corn  per  acre. 


.fcn^n^  pup  //np's^Lfjui  ui  HPjuiey 


Rainfall  and  the  Crops  49 

divided  by  the  area  included  between  the  curve  and  the 
straight  Hne  indicating  the  mean  value  of  the  observa- 
tions. In  the  equation  to  the  compound  cycle  describ- 
ing the  typical  curve  with  which  we  shall  have  to  deal, 
the  first  term  gives  the  mean  value  of  the  observations, 
and  the  remaining  four  harmonic  terms  trace  the  area 
about  the  horizontal  line  drawn  at  a  distance  from  the 
base  line  equal  to  the  mean  value  of  the  observations. 
The  reason  for  adopting  this  complex  coefficient  K  is 
that  the  curves  whose  relative  degrees  of  fit  are  in 
question  apply  to  qualitatively  different  things.  From 
the  method  of  calculating  K,  it  follows  that  the  smaller 
the  value  of  K,  the  better  is  the  degree  of  fit  of  the  curve 
to  the  observations. 

Passing  now  to  the  calculations  referring  to  the 
representative  crops,  we  find, 

For  potatoes,  the  correlation  of  the  yield  per  acre 
with  the  rainfall  of  its  critical  period — July  and  Au- 
gust— is  r  =  .666.  The  measure  of  the  fit  of  the  com- 
pound cycle  of  thirty-three  years  and  eight  years  with 
their  semiharmonics  is,  in  case  of  the  yield  per  acre, 
K  =  1.97,  and  in  case  of  the  rainfall  of  the  critical  period 
of  growth,  K  =  1.30. 

For  hay,  the  correlation  of  the  yield  per  acre  with 
the  rainfall  of  its  critical  period — March,  April,  May, 
June — is  r  =  .620.  The  measure  of  the  fit  of  the  com- 
pound cycle  to  the  data  is,  in  case  of  the  yield  per  acre, 
K  =  1.57,  and  in  case  of  the  rainfall  of  the  critical  season, 

For  corn,  the  correlation  of  the  yield  per  acre  with 


50  Economic  Cycles:  Their  Law  and  Cause 

the  rainfall  of  the  critical  season — July  and  August — 
is  r  =  .589.  The  measure  of  the  fit  of  the  compound 
cycle  to  the  data  is,  for  the  yield  per  acre,  K  =  \.52, 
and,  for  the  rainfall  of  the  critical  season,  K  =  1 .30. 

For  oats,  the  computation  of  the  equation  has  not 
been  carried  out  because  no  critical  period  of  growth 
could  be  found  in  which  the  correlation  between  yield 
and  rainfall  was  higher  than  r  =  .3.  The  correlations 
were,  for  March,  r  =  — .181;  for  April,  r  =  — .147;  for 
May,  r  =  120;  for  June,  r  =  .297;  for  July,  r  =  .140;  for 
May,  June,  and  July,  r  =  .290. 

Referring  now  to  the  Figures  11,  12,  13  and  to  the 
calculations  that  have  just  been  reviewed,  we  observe 
that  the  compound  cycles  of  yield  per  acre  and  of  the 
rainfall  of  the  critical  seasons  flow  almost  congruently, 
and  that  the  compound  cycle  of  thirty-three  years 
and  eight  years  with  their  semiharmonics  fits  the  yield 
data  nearly  as  well  as  it  fits  the  rainfall  data. 

Cycles  in  the  Index  of  Crop  Fluctuations  and  in  the  Cor- 
respondirig  Index  of  Mean  Effective  Rainfall 

Does  the  cyclical  movement  of  rainfall  give  a  rhyth- 
mic movement  to  the  fluctuations  in  the  yield  of  the 
crops  taken  all  together?  The  preceding  section  has 
treated  the  relation  of  the  yield  of  the  separate  crops 
to  the  rainfall  of  their  respective  critical  seasons;  we 
now  inquire  whether  the  yield  of  all  of  the  crops  taken 
together  shows  a  tendency  to  conform  to  the  cycUcal 
movement  of  rainfall.  In  order  to  answer  this  question 
two  preUminary  steps  must  be  taken:  (1)  A  method 


Rainfall  and  the  Crops  51 

must  be  devised  for  measuring  the  fluctuation  in  the 
yield  of  the  crops  when  the  crops  are  taken  all  together; 
and  (2)  a  method  must  be  devised  for  combining  the 
rainfall  of  the  critical  periods  of  the  growth  of  the 
several  crops.  These  two  steps  we  shall  now  consider. 
In  regard  to  the  first  of  these  desiderata,  it  is  clear 
that  the  measure  of  the  fluctuation  of  crops  taken  as  a 
whole  should  be  based  upon  the  best  measure  of  the 
fluctuation  of  the  yield  of  the  crops  taken  singly.  More- 
over, there  is  a  general  agreement  that  the  standard 
deviation  of  a  frequency  scheme  is  a  good  measure  of 
the  scatter  of  the  observations  about  their  mean  value. 
A  natural  step,  therefore,  would  be  to  assume  that  if 
the  observations  form  a  series  in  time,  a  good  rela- 
tive measure  of  their  fluctuations  at  different  epochs  is 
afforded  by  the  ratio  of  the  deviations  of  the  observa- 
tions from  their  mean  divided  by  the  standard  devia- 
tion. For  example,  the  mean  yield  of  oats  in  Illinois, 
for  the  period  1870  to  1910,  was  31.4  bushels  per  acre, 
and  the  standard  deviation  of  the  yield  for  the  same 
period  of  time  was  cr  =  5.2  bushels.  The  yield  per  acre 
for  the  year  1910  was  38.0  bushels.  If  A  be  taken  to  rep- 
resent the  deviation  of  the  yield  of  any  year  from  the 
mean  yield  of  the  whole  period,  then  the  A  for  1910  was 
38.0-31.4=6.6,    and    the    fluctuation    for    1910   was 

-  =  -^  =  1.27.     Similarly,  for  the  year  1908,  when  the 
o-       5.2 

A 
yield  was  23.0  bushels,  the  fluctuation  was,  -  =  -  l.()2. 

It  happens  that  in  the  case  of  oats,  there  is  no  secular 
trend  to  the  yield,  but  when  the  secular  trend  exists. 


52  Economic  Cycles:  Their  Law  and  Cause 

it  must  be  eliminated  before  the  fluctuation  is  com- 
puted. 

In  Table  III  of  the  Appendix  to  this  chapter  the 
fluctuation  for  each  of  the  forty-one  years  1870-1910 
is  given  for  corn,  oats,  hay,  and  potatoes.  By  taking 
the  algebraic  sum  of  the  fluctuations  for  all  the  crops 
for  any  given  year  and  dividing  by  four — the  number  of 
the  crops — a  measure  of  the  fluctuation  of  the  crops 
taken  all  together  is  obtained.  This  measure  we  shall 
refer  to  as  the  index  of  the  fluctuation  of  crops.  The 
index  for  each  of  the  years  1870-1910  is  recorded  in  the 
last  column  of  Table  III. 

The  index  of  crop  fluctuation  computed  in  the  man- 
ner that  has  just  been  described  is  regarded  as  a  more 
accurate  measure  of  the  fluctuation  of  crops  than 
would  be  obtained  from  an  index  formed  by  taking  as 
the  fluctuation  for  each  year,  in  case  of  each  crop,  the 
ratio  of  the  deviation  from  the  mean  divided  by  the 
mean.  If  the  crops  differ  in  their  coefficients  of  varia- 
tion, that  is  to  say,  if  the  ratio  ^j,  where  M  is  the  mean 

yield  and  cr  is  the  standard  deviation,  is  not  the  same 
for  all  crops,  then  the  crop  with  the  largest  coefficient  of 
variation  would  receive  the  largest  weight  in  the  general 
index.     The  coefficients  of  variation  for  the  crops  in 

our  Table  are,  for  corn,  ^^;f~--  =.217;  for  oats,  ^~~  = 

2b. 93  .31.44 

.104;  for  hay,  j^  =  .137;  for  potatoes,  ^||^  =  ..330.    If 

the  usual  method  of  forming  index  numbers  were  em- 
ployed in  this  case  to  measure  crop  fluctuations,  the 


Rainfall  and  the  Crops  53 

several  crops  would,  in  consequence  of  their  different 
variabilities,  receive  disproportionate  weights.  The 
method  of  calculating  the  index  which  we  have  em- 
ployed obviates  this  difficulty. 

Having  now  obtained  an  index  of  the  fluctuation  of 
crops,  we  next  consider  the  method  of  combining  the  rain- 
fall of  the  critical  periods  of  growth  for  the  several  crops. 
The  method  will  be  clear  if  we  bear  in  mind  that  the 
critical  period  of  growth  of  a  crop  is  the  combination  of 
months  whose  rainfall  gives  the  highest  correlation  with 
the  yield.  The  mean  effective  monthly  rainfall  for  the 
critical  period  of  a  crop  is  the  total  rainfall  of  the  critical 
period  of  growth  divided  by  the  number  of  months  mak- 
ing up  the  critical  period.  In  case  of  hay,  for  example, 
the  critical  period  of  growth  is  March,  April,  May, 
June.  The  mean  effective  rainfall  for  any  given  year 
would  be  the  total  rainfall  for  the  four  months,  March, 
April,  May,  June,  divided  by  the  number  of  the  months. 
If  the  mean  effective  monthly  rainfall  for  the  several 
crops  is  summed  for  each  year  and  divided  by  the  num- 
ber of  crops,  a  measure  is  obtained  of  the  mean  effective 
monthly  rainfall  for  the  crops  taken  all  together.  In 
Table  IV  of  the  Appendix  to  this  chapter  the  mean 
effective  rainfall  of  the  several  crops,  and  of  the  crops 
taken  all  together,  is  tabulated  for  each  of  the  years 
1870-1910. 

We  have  now  an  index  of  the  fluctuation  of  crops  and 
an  index  of  the  mean  effective  rainfall  of  the  critical 
periods  of  the  crops.  The  correlation  between  the 
two  series  is  r  =  .584.    In  Figure  14  are  traced  the  graphs 


54 


Economic  Cycles:  Their  Law  and  Cause 


Index  of  flu  cfua  tion  of  crops. 


/lPj.uiej  /(jLi4.uouj  3ai4.03jI^s  ups^a^ 


Rainfall  and  the  Crops  55 

of  the  compound  cycles  that  describe  the  two  series, 
each  graph  consisting  of  two  cycles  and  their  semi- 
harmonics,  a  thirty-three  years  cycle  describing  the 
ground-swell  and  the  smaller  cycle  of  eight  years  sum- 
marizing the  minor  cyclical  movements.  The  measure 
of  the  degree  of  fit  to  the  observations  is,  in  case  of  the 
yield  curve,  K  =2.46,  and  in  case  of  the  rainfall  curve, 
K  =  1.68.  The  yield  curve  reproduces  the  general 
characteristic  features  of  the  rainfall  curve. 

Our  findings  with  reference  to  the  crops  taken  to- 
gether are  similar  to  what  we  discovered  in  case  of  the 
single  crops:  The  yield  per  acre  and  the  rainfall  of  the 
critical  season  are  highly  correlated;  the  rhythmical 
movements  of  the  yield  and  of  the  effective  rainfall 
may  be  accurately  described  by  a  compound  cycle  of 
thirty-three  years  and  eight  years  with  their  semi- 
harmonics;  and  the  yield  curve  reproduces  the  general 
characteristics  of  the  curve  of  effective  rainfall. 

Passing  now  to  a  summary  of  the  contents  of  this 
chapter,  we  may  collect  our  results  in  a  series  of  prop- 
ositions. 

(1)  The  yield  per  acre  of  the   four  representative 

crops,  corn,  hay,  oats,  and  potatoes  is  associ- 
ated with  the  amount  of  the  rainfall  of  their 
respective  critical  periods  of  growth.  In 
three  out  of  the  four  cases  the  degree  of  cor- 
relation lies  between  r  =  .589  and  r  =  .666. 

(2)  The  rhythmical  changes  in  the  yield  per  acre  of 

the  crops  and  in  the  rainfall  of  the  respective 


56  Economic  Cycles:  Their  Law  and  Cause 

critical  seasons  may  both  be  accurately  de- 
scribed by  a  compound  cycle  composed  of  a 
thirty-three  years  cycle  with  its  semihar- 
monic,  which  summarizes  the  ground-swell  of 
the  movement,  and  a  superposed  cycle  of  eight 
years  with  its  semiharmonic,  describing  the 
shorter  rhythmical  movements. 

(3)  In  three  of  the  four  representative  crops,  the 

compound  cycles  summarizing  the  changes  in 
the  rainfall  of  the  critical  periods  of  growth 
and  the  changes  in  the  yield  per  acre  of  the 
crops  are  so  nearly  congruent  that,  consider- 
ing the  high  correlation  of  the  yield  with  the 
rainfall,  one  may  conclude,  with  a  high  degree 
of  probability,  that  the  rhythmical  movement 
in  the  weather  conditions  represented  by 
rainfall  is  the  cause  of  the  cycles  of  the  crops. 

(4)  The  index  of  the  fluctuation  of  the  crops  taken 

together,  and  the  index  representative  of  the 
mean  effective  rainfall  during  the  critical 
seasons  are  highly  correlated,  r  =  .584. 

(5)  The  rhythmical    changes   in   the    index  of  the 

fluctuation  of  the  crops  and  in  the  index  of 
the  mean  effective  rainfall  are  accurately 
described  by  a  compound  cycle  which  is  made 
up  of  a  thirty-three  years  cycle  and  an  eight 
years  cycle  with  their  semiharmonics,  and 
these  two  compound  curves  are,  in  their  gen- 
eral characteristics,  much  alike. 

(6)  The  investigation  of  the  crops  taken  singly  and 


Rainfall  and  the  Crops  57 

taken  together  leads  to  the  general  conclu- 
sions : 

(a)  that  there  is  a  rhythmical  movement 
in  both  the  yield  of  the  crops  and  in  the 
rainfall  of  the  critical  periods  which  is 
summarized  in  a  compound  cycle,  in 
which  the  constituent  elements  are  a 
ground-swell  of  thirty-three  years  and 
its  semiharmonic,  and  a  shorter  super- 
posed cycle  of  eight  years  with  its 
semiharmonic ; 

(b)  that  the  cyclical  movement  in  the 
weather  conditions  represented  by  rain- 
fall is  the  fundamental,  persistent  cause 
of  the  cycles  of  the  crops. 


APPENDIX 


TABLE  I. — The  Crops  op  Illinois 


Year 

Yield  Per  Acre  of 
Corn,  in  Bushels 

Yield  Per  Acre  of 
Potatoes,  in  Bushels 

Yield  Per 

Acre  of 

Hav,  in 

Tons 

Ton  =  2000 

lbs. 

Yield  Per 
Acre  of 
Oats,  in 
Bushels 

Actual 
Yield 

Reduced 
Yield 

Actual 
Yield 

Reduced 

YiEID 

1870 

35.2 

35.2 

81 

81.0 

1.18 

26.0 

1871 

38.3 

38.1 

61 

60.8 

1.31 

33.1 

1872 

39.8 

39.4 

75 

74.5 

1.35 

36.6 

1873 

21.0 

20.4 

40 

39.3 

1.25 

30.0 

1874 

18.0 

17.2 

55 

54.1 

1.20 

17,5 

1875 

34.3 

33.3 

128 

126.8 

1.37 

33.0 

1876 

25.0 

23.8 

75 

73.6 

1.40 

20.0 

•    1877 

29.0 

27.6 

93 

91.4 

1.60 

37.0 

1878 

27.1 

25,5 

67 

65.1 

1.49 

35.9 

1879 

35.0 

33.2 

88 

85.9 

1.21 

32.0 

1880 

27.2 

25.2 

75 

72.7 

1.45 

31.8 

1881 

19.4 

17.2 

48 

45.4 

1.30 

33.4 

1882 

23.0 

20.6 

85 

81.8 

1.25 

40.7 

1883 

25.0 

22.4 

92 

89.0 

1.45 

36.1 

1884 

30.0 

27.1 

79 

75.7 

1.40 

32.8 

1885 

31.4 

28.3 

87 

83.5 

1.30 

32.8 

1886 

24.5 

21.2 

67 

63.3 

1.34 

31.8 

1887 

19.2 

15.7 

33 

29.0 

.80 

29.5 

1888 

35.7 

32.0 

80 

75.8 

1.40 

35.  S 

1889 

32.3 

28.4 

99 

94.6 

1.39 

37.5 

1890 

26.2 

22. 1 

30 

25.3 

1.30 

21.0 

1891 

33.5 

29.2 

92 

87.1 

1.25 

34,0 

1892 

26.2 

21.7 

52 

46.9 

1.25 

26.3 

1893 

25.7 

21.0 

53 

47.6 

1.21 

27.2 

1894 

28.8 

23.9 

50 

44.4 

1.14 

36.1 

1895 

37.4 

32.3 

77 

71.2 

.66 

24.4 

1896 

40.5 

35.2 

97 

90.9 

1.38 

28.0 

1897 

32.5 

27.0 

38 

31.7 

1.29 

32.0 

1898 

30.0 

24.3 

70 

63.5 

1.56 

29.0 

1899 

36.0 

30.1 

96 

89.2 

1.29 

38.0 

1900 

37.0 

30.9 

90 

83.0 

1.27 

38.0 

1901 

21.4 

15.1 

35 

27.8 

1.08 

28.2 

1902 

38.7 

32.2 

118 

110.5 

1.50 

37.7 

1903 

32.2 

25.5 

72 

64.3 

1.54 

26.6 

1904 

36 . 5 

29.6 

108 

100.1 

1.36 

32.0 

1905 

39.8 

32.7 

75 

66.8 

1.35 

35.5 

1906 

30.1 

28.8 

97 

88.6 

.98 

29.5 

1907 

36.0 

28.4 

87 

78.4 

1.40 

24.5 

1908 

31.6 

23.8 

71 

62.2 

1.53 

23.0 

1909 

35.9 

27.9 

91 

81.9 

1.45 

36.6 

1910 

39.1 

30.9 

75 

65.7 

1.33 

38.0 

58 


Rainfall  and  the  Crops 


59 


TABLE  II. — Mean  Monthly  Rainfall  in  Illinois 


Mean  Monthly  R 

AINFALL 

Year 

March 

April 

Mat 

June 

July 

August 

Septem- 
ber 

1870 

3.92 

1.43 

1.64 

1.93 

2.85 

3,95 

3.69 

1871 

3.31 

2.47 

3.06 

4.00 

3.11 

3.50 

1.22 

1872 

2.59 

3.39 

3.60 

5.68 

5.00 

3,65 

4.29 

1873 

1.75 

4.98 

4.87 

2.18 

3.99 

1.77 

3.19 

1874 

2.39 

3.50 

2.25 

3.45 

2.06 

4,28 

3.95 

1875 

2.83 

2.60 

4.57 

5.36 

9.37 

1,96 

4,60 

1876 

5.13 

3.38 

4.68 

5.53 

4.91 

3,83 

4.33 

1877 

4.02 

3.53 

3.13 

7.39 

3,27 

2.78 

2.29 

1878 

3.04 

4.66 

5.04 

2.72 

3.83 

4.10 

1.61 

1879 

2.59 

2.42 

2.10 

4,33 

3.44 

4.89 

1.48 

1880 

3.31 

4.29 

5.93 

3.53 

3.10 

3.65 

3.59 

1881 

3.16 

2.18 

2.26 

5.93 

2.58 

0.84 

4.04 

1882 

4.00 

4.00 

6.60 

6.61 

3.46 

4.65 

2.08 

1883 

1.81 

4.16 

5.38 

5.51 

4.86 

1.86 

0.88 

1884 

3.31 

3,36 

4.40 

5.13 

4.09 

2.40 

4.80 

1885 

0.53 

4.13 

3.03 

5.63 

2.80 

5.06 

5.67 

1886 

3.02 

3.60 

4.07 

4.42 

1.15 

3.86 

4.81 

1887 

2.37 

2.46 

2.90 

1.94 

2.40 

2.46 

3.25 

1888 

4.09 

1.94 

5.18 

4.80 

3.83 

4.31 

1.46 

1889 

1.62 

2.00 

5,11 

5.35 

4.45 

1.22 

3.78 

1890 

4.34 

3.75 

3.86 

4.58 

2.03 

2.96 

3.04 

1891 

3.43 

2,91 

2.19 

4.11 

1.88 

4,71 

1.02 

1892 

2.17 

6.43 

8,06 

5.77 

3.71 

3.03 

2.01 

1893 

3.31 

7.64 

4.24 

3.51 

2.20 

0.96 

3.09 

1894 

2.98 

2.73 

3.29 

2.31 

1.58 

1.74 

4.53 

1895 

1.72 

2,17 

2.34 

2.68 

6.01 

2.76 

3,00 

1896 

1.90 

2.84 

6.09 

4.14 

6.17 

2.95 

5 ,  79 

1897 

6.22 

4.53 

1.94 

4.28 

3.59 

1.19 

0.99 

1898 

7.70 

3.47 

6.26 

4.71 

2.84 

4.70 

5 .  07 

1899 

3.19 

1.64 

6.41 

3.00 

3,42 

2.70 

2,23 

1900 

2.12 

1.64 

4.51 

4.31 

4.15 

3,72 

3,59 

1901 

3.80 

1.84 

1.86 

3,55 

2,63 

1,91 

1,97 

1902 

3.64 

2.55 

3.78 

7.77 

4,78 

4.67 

4.24 

1903 

3.23 

4.51 

3.25 

3.03 

3.41 

4.58 

3.85 

1904 

6.41 

3.76 

3.29 

3.28 

5.23 

4.25 

5.43 

1905 

2.32 

3.88 

4.27 

3.69 

4.78 

3.41 

2.89 

1906 

4.09 

2.09 

2.39 

3.08 

2.58 

4,15 

5.15 

1907 

3.26 

2.89 

3.95 

4.17 

5.39 

5 ,  56 

2.38 

1908 

3.21 

4.59 

8.07 

3.14 

3.32 

2 ,  39 

1.41 

1909 

2.62 

5.94 

4.23 

4.04 

4 ,  96 

2,12 

4.25 

1910 

0.32 

3,66 

5.04 

2,62 

4.72 

2.51 

4.61 

60 


Economic  Cycles:  Their  Law  and  Cause 


TABLE  III. — Index  of  Fluctuation  of  Crops.  A  =  Devia- 
tion FROM  THE  Mean  after  the  Secular  Trend  has  been 
Eliminated,    cr  =  Standard  Deviation 


Corn 

Oats 

Hay 

Pota- 

Sum op 

Sum  of 

Index 

1      of 

Year 

A 

A 

A 

toes 
A 

Positive 

Negative 

Differ- 

: Fluct- 

— 

— 

— 

Fluctua- 

Fluctu-a- 

ence 

uation 

cr 

cr 

(T 

<r 

tions 

TIONS 

OF 

Crops 

1870 

1.43 

—1.04 

—   .72 

.45 

1.88 

1.76 

+    .12 

+    .03 

1871 

1.93 

.33 

.00 

—   .42 

2.26 

.42 

+  1.84 

+   .46 

1872 

2.16 

1.00 

.22 

.17 

3.55 

.00 

+3.55 

+    .89 

1873 

—1.12 

—   .27 

—  .33 

—1.34 

.00 

3.06 

—3.06 

—  .76 

1874 

—1.67 

—2.67 

—  .61 

—  .70 

.00 

5.65 

—5.65 

—1.41 

1875 

1.10 

.31 

.33 

2.42 

4.16 

.00 

+4.16 

+  1.04 

1876 

—  .67 

—2.19 

.50 

.13 

.63 

2.86 

—2.23 

—  .56 

1877 

.12 

1.08 

1.61 

.90 

3,71 

.00 

+3.71 

+   .93 

1878 

—  .24 

.87 

1.00 

—  .23 

1,87 

.47 

+  1.40 

+   .35 

1879 

1.09 

.12 

—   .56 

.66 

1.87 

.56 

+  1.31 

+    .33 

1880 

—   .29 

.08 

.78 

.09 

.95 

.29 

+   .66 

+   .16 

1881 

—1.69 

.38 

—  .06 

—1.08 

.38 

2.83 

—2.45 

—  .61 

1882 

—1.09 

1,79 

—  .33 

.48 

2.27 

1.42 

+   .85 

+    .21 

1883 

—  .78 

.90 

.78 

.79 

2.47 

.78 

+  1.69 

+    .42 

1884 

.03 

.27 

.50 

.22 

1.02 

.00 

+  1.02 

+    .25 

1885 

.24 

.27 

—  .06 

.56 

1.07 

.06 

+  1.01 

+    .25 

1886 

—  .98 

.08 

.17 

—  .31 

.25 

1.29 

—1.04 

—   .26 

1887 

—1.93 

—  .37 

—2.83 

—1.78 

.00 

6.91 

—6.91 

—1.73 

1888 

.88 

.85 

.50 

.23 

2.46 

.00 

+2.46 

+    .61 

1889 

.26 

1.17 

.44 

1.03 

2,90 

.00 

+2.90 

+    .72 

1890 

—1.00 

—2.00 

—  .06 

—1.94 

.00 

5.00 

—5.00 

—1.25 

1891 

.40 

.50 

—  .33 

.71 

1.61 

.33 

+  1.28 

+    .32 

1892 

—  .90 

—  .98 

—  .33 

—1.01 

.00 

3.22 

—3.22 

—  .80 

1893 

—1.02 

—  .81 

—  .56 

—  .98 

.00 

3.37 

—3.37 

—  .84 

1894 

—  .52 

.90 

—  .94 

—1.12 

.90 

2.58 

—1.68 

—   .42 

1895 

.93 

—1.35 

—3.61 

.03 

.96 

4.96 

—4.00 

—1.00 

1896 

1.43 

—   .65 

.39 

.88 

2,70 

.65 

+2.05 

+    .51 

1897 

.02 

.12 

—  .11 

—1.67 

,14 

1.78 

—1.64 

—   .41 

1898 

—   .45 

—  .46 

1.39 

—  .30 

1.39 

1.21 

+    .18 

+    .05 

1899 

.55 

1.27 

—  .11 

.80 

2,62 

.11 

+2.51 

+    .63 

1900 

.69 

1.27 

— ■  .22 

.54 

2.50 

.22 

+2.28 

+    .57 

1901 

—2.03 

—   .62 

— 1.2S 

—1.83 

.00 

5 ,  76 

—5.76 

—1.44 

1902 

.91 

1.21 

1.00 

1,72 

4.90 

,00 

+4.90 

+  1.22 

1903 

—   .24 

—   .92 

1.28 

—   .27 

1.28 

1,43 

—  .15 

—  .04 

1901 

.47 

.12 

.2'^ 

1,27 

2.14 

.00 

+2.14 

+    .54 

1905 

1.00 

.79 

.22 

—  .16 

2.01 

.16 

+  1.85 

+   .46 

1903 

.31 

—  .37 

—1.83 

.78 

1.09 

2,20 

—1.11 

—  .28 

1907 

.26 

—1.33 

.50 

.34 

1.10 

1,33 

—  .23 

—   .06 

1908 

—  .53 

—1.62 

1.22 

—  .36 

1.22 

2,51 

—1,29 

—  .32 

1909 

.17 

1.00 

.78 

.49 

2.44 

.00 

+2,44 

+   .61 

1910 

.69 

1.27 

.11 

—   .21 

2.07 

.21 

+  1.86 

+   .46 

Rainfall  and  the  Crops 


61 


TABLE  IV. — Mean  Effective  Monthly  Rainfall  in  Illinois 


! 

Mean  Effective  Monthly  Rainfall 

Mean 
Effective 
Monthly 
Rainfall 
for  Crops 

Year 

For 
Corn 

For 
Oats 

For 
Hay 

For 
Potatoes 

Sum  of 
Preceding 
Columns 

1870 

3.40 

2.14 

2.23 

3.40 

11.17 

2.79 

1871 

3.30 

3.39 

3.21 

3.30 

13.20 

3.30 

1872 

4.33 

4.76 

3.81 

4.33 

17.23 

4.31 

1873 

2.88 

3.68 

3.45 

2.SS 

12.89 

3.22 

1874 

3.17 

2.59 

2.90 

3.17 

11.83 

2.98 

1875 

5.66 

6.43 

3.84 

5.66 

21.59 

5.40 

1876 

4.37 

5.04 

4.68 

4.37 

18.46 

4.61 

1877 

3.02 

4.60 

4.52 

3.02 

15.16 

3.79 

1878 

3.96 

3.86 

3.86 

3.96 

15.64 

3.91 

1879 

4.16 

3.29 

2.86 

4.16 

14.47 

3.62 

ISSO 

3.37 

4.19 

4.26 

3.37 

15.^9 

3.80 

1881 

1.71 

3.58 

3.38 

1.71 

10.3.^ 

2.59 

1882 

4.05 

5.56 

5.30 

4.05 

18.96 

4.74 

1883 

3.36 

5.25 

4.20 

3.36 

16.17 

4.04 

1884 

3.25 

4.54 

4.05 

3.25 

15.09 

3.77 

1885 

3.93 

3.82 

3.33 

3.93 

15.01 

3.75 

1886 

2.51 

3.21 

3.78 

2.51 

12.01 

3.00 

1887 

2.43 

2.41 

2.42 

2.43 

9.69 

2.42 

1888 

4.07 

4.60 

4.00 

4.07 

16.74 

4.18 

1889 

2.84 

4.97 

3.52 

2.84 

14.17 

3.54 

1890 

2.50 

3.49 

4.13 

2.50 

12.62 

3.15 

1891 

3.29 

2,73 

3.16 

3.29 

12.47 

3.12 

1892 

3.37 

5. 85 

5.61 

3.37 

18.20 

4.55 

1893 

1.58 

3.32 

4.67 

1.58 

11.15 

2.79 

1894 

1.66 

2.39 

2.83 

1.66 

8.54 

2.14 

1895 

4.38 

3.68 

2.23 

4.38 

14.67 

3.67 

1896 

4.56 

5.47 

3.74 

4.56 

18.33 

4.58 

1897 

2.39 

3.27 

4.24 

2.39 

12.29 

3.07 

1898 

3.77 

4 .  60 

5.53 

3.77 

17.67 

4.42 

1899 

3.06 

4.2S 

3.56 

3.06 

13.96 

3.49 

1900 

3.93 

4.32 

3.15 

3.93 

15.33 

3.83 

1901 

2.27 

2.68 

2.76 

2.27 

9.98 

2.50 

1902 

4.72 

5.44 

4.43 

4.72 

19.31 

4.83 

1903 

4.00 

3.23 

3.50 

4.00 

14.73 

3.68 

1904 

4.74 

3.93 

4.18 

4.74 

17.59 

4.40 

1905 

4.09 

4.25 

3.54 

4.09 

15.97 

3.99 

1906 

3.36 

2.68 

2.91 

3.36 

12.31 

3.08 

1907 

5.47 

4.50 

3.57 

5.47 

19.01 

4.75 

1908 

2.85 

4.84 

4.75 

2.85 

15.29 

3.82 

1909 

3.54 

4.41 

4.22 

3.54 

15.71 

3.93 

1910 

3.61 

4.13 

2.91 

3.61 

14.26 

3.56 

CHAPTER  IV 

THE  LAW  OF   DEMAND 

Kann  man  nicht  die  Nachfragefunktion  genauer  feststellen,  so 
genau,  dass  wiv  nicht  bloss  ein  eindeutiges,  sondern  ein  konkretes 
Resultat  gewinnen?  Ich  glaube  die  Antwort  zu  horen:  Welch' 
ein  phantastisches  Unterfangen-Unberechenbarkeit  der  wirtschaft- 
lichen  Vorgange — steter  Wechsel — u.  s.  w! 

Joseph  Schumpeter. 

Questions  affecting  for  the  most  part  the  supply  of 
commodities  have  thus  far  been  the  object  of  our  in- 
vestigation, but  the  inquiry  as  to  the  cause  and  law  of 
economic  cycles  must  extend  to  a  consideration  of 
cycles  of  values  and  prices.  Since  the  rhythmical 
variation  in  the  supply  of  crops  produces  its  effect  upon 
crop  prices  in  accordance  with  the  laws  of  demand  for 
the  several  crops,  the  obvious  first  and  necessary  step 
in  bringing  the  results  of  the  preceding  chapters  to  bear 
upon  the  question  of  the  cause  and  law  of  economic 
cycles  is  to  solve  the  problem  of  the  relation  between 
the  variations  in  the  supply  of  the  several  crops  and 
the  resulting  variations  in  their  respective  prices.  It 
is  required  to  derive  from  existing  data  the  concrete 
laws  of  demand  for  the  representative  crops. 

The  Theory  of  Demand 

The  mathematical  treatment  of  the  theory  of  demand 
furnishes  two  doctrines  that  are  of  importance  in  our 

62 


The  Law  of  Demmid 


63 


Figure  15.  The  law  of  demand. 


subsequent  work :  The  doctrine  of  the  uniformity  of  the 
demand  function  and  the  doctrine  of  the  elasticity  of 
demand.  The  exposition  of  these  two  doctrines  will  be 
faciUtated  by  reference  to  Figure  15,  in  which,  accord- 
ing to  the  usual  practice,  quantities  of  commodity  are 
measured  upon  the  axis 
of  abscissas,  and  the  cor- 
responding prices  per 
unit,  upon  the  axis  of 
ordinates. 

The  doctrine  of  the 
uniformity  of  the  demand 
function,  which  is  trace- 
able to  Cournot,^  but  is 
especially  stressed  by 
Professor  Mar.shall,  has  been  put  in  these  words: 
"There  is  then  one  general  laiv  of  demand  viz.,  that 
the  greater  the  amount  to  be  sold,  the  smaller  will 
be  the  price  at  which  it  will  find  purchasers ;  or,  in  other 
words,  that  the  amount  demanded  increases  with  a 
fall  in  price  and  diminishes  with  a  rise  in  price."    Re- 

1  Cournot:  Recherches  sur  les  principes  mathematiqties  de  la  theorie 
des  richesses,  §§21,  22.  Assuming  that  the  relation  between  price 
and  the  amount  demanded  is  represented  by  F(p),  he  says,  p.  54: 
"Si  la  fonction  F(p)  est  continue,  elle  jouira  dc  la  propri^t6  conmiune 
a  toutes  les  fonctions  de  cette  nature,  et  sur  laquellc  reposent  tant 
d'appHcations  important es  de  I'analyse  mathematique:  les  varia- 
tions de  la  demande  seront  sensiblement  proportionelles  aux  varia- 
tions du  prix,  tant  que  celles-ci  seront  de  petites  fractions  du  prix 
originaire.  D'ailleurs,  ces  variations  seront  de  signes  contraires, 
c'est-5,-dire  qu'k  une  augmentation  de  prix  correspondra  une  dimi- 
nution de  la  demande." 


64  Economic  Cycles:  Their  Law  and  Cause 

f erring  to  Figure  15,  this  statement  means  tliat  if  at 
any  point  in  the  demand  curve  DD',  say  the  point  P, 
a  straight  hue  is  drawn  tangent  to  the  curve,  then  the 
trigonometric  tangent  of  the  angle  which  the  hne  makes 
with  the  positive  direction  of  the  axis  of  x,  is  negative. 
In  Professor  Marshall's  words:  "The  one  universal 
rule  to  which  the  demand  curve  conforms  is  that  it  is 
inclined  negatively  throughout  the  whole  of  its  length."^ 
As  we  proceed  we  shall  find  that  the  law  of  demand  for 
some  commodities  does  indeed  conform  to  the  type  of 
curve  which  has  just  been  described,  but  it  will  be  a  part 
of  the  work  of  the  next  chapter  to  show  that  the  doc- 
trine of  the  uniformity  of  the  demand  function  is  an 
idol  of  the  static  state — of  the  method  of  costeris 
-paribus — which  has  stood  in  the  way  of  the  successful 
treatment  of  concrete  dynamic  problems. 

Assuming  that  the  law  of  demand  for  a  given  com- 
modity is  represented  by  the  descending  curve  DD'  in 
Figure  15,  the  elasticity  of  demand  for  the  commodity 
when  OM  units  ai'e  bought  is  measured  by  the  ratio 

7)  l7  "^  PM  "^h^^  ^^  ^^  ^^y>  ^^^  general  terms,  if  the  price 
of  the  commodity  undergoes  a  small  change,  the  amount 
of  the  commodity  that  is  demanded  likewise  undergoes 
a  small  change,  and  the  degree  of  the  elasticity  of  de- 
mand for  the  commodity,  in  the  given  state  of  the  mar- 
ket, is  measured  by  the  ratio  of  the  relative  change  in 

'  Marshall:  Priiiciples  of  Economics,  4th  edit.,  pp.  174,  174  note  2. 
In  the  subsequent  reasoning  we  shall  call  this  tyj^e  of  dcn^and 
curve  the  negative  type. 


The  Laiv  of  Demand  65 

the  amount  demanded  to  the  small  relative  change  in 
the  price.  Or,  more  definitely,  if  "a  fall  of  1  per  cent. 
in  price  would  cause  an  increase  of  2  per  cent,  in  the 
amount  demanded,  the  elasticity  of  demand  would  be 
two;"  if  "a  fall  of  1  per  cent,  in  price  would  cause  an 
increase  of  /g  per  cent,  in  the  amount  demanded,  the 
elasticity  of  demand  would  be  one-third;  and  so  on."  ^ 
It  will  be  observed  that  the  theory  of  elasticity  of 
demand  in  this  classical  form  is  presented  from  the 
point  of  view  of  infinitesimal  changes  in  the  two  va- 
riables — ,  price  and  commodity  demanded.  It  gives 
the  degree  of  elasticity  of  demand  for  a  point  in  time, 
for  a  given  state  of  the  market  assuming  all  other 
things  to  remain  the  same ;  and  for  this  reason  it  may  be 
said  to  treat  of  elasticity  of  demand  from  a  statical 
point  of  view.  But  this  is  not  its  most  serious  limitation. 
It  postulates  a  knowledge  of  the  demand  curve,  and 
while  it  gives  an  exposition  of  the  method  by  which  the 
degree  of  elasticity  of  demand  might  be  determined 
provided  the  demand  curve  were  known,  there  have 
been  grave  doubts  as  to  whether  the  practical  difficulty 
of  deriving  the  demand  curve  would  ever  be  overcome. 

The  problem  before  us  is  to  derive  the  demand  curve 
from  statistics;  to  measure  the  degree  in  which  it  is  an 
accurate  description  of  the  changes  of  actual  industry; 
and  to  give  the  numerical  coefficients  of  elasticity  of 
demand  for  typical  commodities. 

1  Marshall:  Principles  of  Economics,  4th  edit.,  pp.  177-178, 
note. 


66  Economic  Cycles:  Their  Law  and  Cause 

Statistical  Laws  of  Demand 

Two  fundamental  defects  in  the  current  theoretical 
method  of  treating  economic  questions  are  exemplified 
in  the  case  of  the  theory  of  demand:  first,  the  assump- 
tion is  made  that  all  other  things  being  equal  (the  old 
cceteris  paribus),  an  increase  in  the  supply  of  the  com- 
modity will  lead  to  a  corresponding  fall  in  the  price; 
secondly,  it  is  assumed  that  the  concrete  problem  of 
the  relation  of  price  and  supply  of  commodity  will  be 
simplified  by  attacking  first  the  constituent  elements 
of  the  question  rather  than  by  attacking  directly  the 
problem  in  its  full  concreteness.  Neither  assumption 
is  satisfactory  nor  indeed  admissible.  The  "other 
things"  that  are  supposed  to  remain  equal  are  seldom 
mentioned  and  are  never  completely  enumerated;  and 
consequently  the  assumption  that,  other  unmentioned 
and  unenumerated  factors  remaining  constant,  the  law 
of  demand  will  be  of  a  certain  type,  is  really  tantamount 
to  saying  that  under  conditions  which  are  unanalyzed 
and  unknown,  the  law  of  demand  will  take  the  supposed 
definite  form.  The  burden  of  proof  is  upon  anyone 
using  this  method  to  show  that  the  assumption  does  not 
at  least  involve  a  physical  impossibility. 

The  second  of  the  above  two  assumptions  is  not  more 
satisfactory  than  the  first.  It  reproduces  the  defects 
of  the  first  assumption  with  others  superadded.  The 
movement  of  prices  results  from  changes  in  many 
factors:  According  to  the  statical  method,  the  method 
of  cceteris  paribus,  the  proper  course  to  follow  in  the 


The  Law  of  Demand  67 

explanation  of  the  phenomenon  is  to  investigate  in 
turn,  theoretically,  the  effect  upon  price  of  each  factor, 
ccBteris  paribus,  and  then  finally  to  make  a  synthesis! 
But  if  in  case  of  the  relation  of  each  factor  to  price  the 
assumption  cceteris  paribus  involves  large  and  at  least 
questionable  hypotheses,  does  one  not  completely  lose 
himself  in  a  maze  of  implicit  hypotheses  when  he  speaks 
of  a  final  synthesis  of  the  several  effects?  We  shall  not 
adopt  this  bewildering  method,  but  shall  follow  the 
opposite  course  and  attack  the  problem  of  the  relation 
of  prices  and  supply  in  its  full  concreteness. 

The  fruitfulness  of  the  statistical  theory  of  correlation 
stands  in  significant  contrast  to  the  vast  barrenness  of 
the  method  that  has  just  been  described,  and  the  two 
methods  follow  opposed  courses  in  dealing  with  a 
problem  of  multiple  effects.  Take,  for  example,  the 
question  of  the  effects  of  weather  upon  crops.  What  a 
useless  bit  of  speculation  it  would  be  to  try  to  solve,  in  a 
hypothetical  way,  the  question  as  to  the  effect  of  rain- 
fall upon  the  crops,  other  unenumerated  elements  of 
weather  remaining  constant?  The  question  as  to  the 
effect  of  temperature,  cceteris  paribus?  How,  finally, 
would  a  synthesis  be  made  of  the  several  individual 
effects?  The  statistical  method  of  multiple  correlation 
formulates  no  such  vain  questions.  It  inquires,  di- 
rectly, what  is  the  relation  between  crop  and  rainfall, 
not  cceteris  paribus,  but  other  things  changing  accord- 
ing to  their  natural  order;  what  is  the  relation  between 
crop  and  temperature,  other  things  conforming  to  the 
observed  changes  in  temperature;  and,  finally,  what  is 


68  Economic  Cycles:  Their  Law  and  Cause 

the  relation  between  crop  and  rainfall  for  constant 
values  of  temperature?  The  problem  of  the  effects  of 
the  constituent  factors  is  solved  only  after  the  more 
general  problem  has  received  its  solution.  This  method 
offers  promise  of  an  answer  to  the  question  as  to  the 
relation  between  the  effective  demand  price  and  the 
supply  of  the  commodity. 

The  chief  difficulties  in  the  computation  of  statistical 
laws  of  demand  are  due  to  changes  that  occur  in  the 
market  during  the  period  to  which  the  statistics  of 
prices  and  of  quantities  of  commodities  refer.  In  order 
that  the  statistical  laws  of  demand  shall  have  sufficient 
validity  to  serve  as  prediction  formulae,  the  observations 
must  be  numerous ;  and  in  order  to  obtain  the  requisite 
number  of  observations,  a  considerable  period  must  be 
covered.  This  usually  means  that,  during  the  interval 
surveyed  in  the  statistical  series,  important  changes 
occur  in  the  condition  of  the  market.  But  in  case 
of  staple  commodities,  such  as  the  agricultural  products 
with  which  we  shall  have  to  deal,  the  effects  of  those 
changes  in  the  condition  of  the  market  that  obscure  the 
relation  between  prices  and  amounts  of  commodity  may 
be  largely  eliminated.  As  far  as  the  law  of  demand  is 
concerned,  the  principal  dynamic  effects  that  need  to 
be  considered  are  changes  in  the  volume  of  the  com- 
modity that  arise  from  the  increasing  population,  and 
changes  in  the  level  of  prices  which  are  the  combined 
result  of  causes  specifically  responsible  for  price  cycles 
and  of  causes  that  produce  a  secular  trend  in  prices. 


The  Law  of  Dernand  69 

The  effects  of  these  two  fundamental  changes  may  be 
eliminated  approximately  by  a  single  statistical  device, 
namely,  by  deducing  the  law  of  demand  from  a  gen- 
eralized treatment  of  the  elasticity  of  demand. 

The  degree  of  elasticity  of  demand,  according  to  the 
classic  formula,  is  measured  by  the  ratio  of  the  relative 
change  in  the  amount  of  the  commodity  that  is  bought 
to  the  relative  change  in  the  price  per  unit  of  the  com- 
modity. Suppose,  now,  that  instead  of  restricting 
this  conception  to  infinitesimal  changes  in  price  and  in 
amount  of  commodity,  we  extend  it  to  the  finite  changes 
that  actually  occur  in  the  market.  Then,  the  relative 
change  in  the  amount  of  commodity  that  is  bought 
may  be  correlated  with  the  relative  change  in  the 
corresponding  price,  and  the  resulting  appropriate 
regression  equation  will  give  the  statistical  law  of 
demand  for  the  coimnodity.  By  taking  the  relative 
change  in  the  amount  of  the  commodity  that  is  de- 
manded, instead  of  the  absolute  quantities,  the  effects 
of  increasing  population  are  approximately  eliminated; 
and  by  taking  the  relative  change  in  the  corresponding 
prices  instead  of  the  corresponding  absolute  prices,  the 
errors  due  to  a  fluctuating  general  price  level  are  par- 
tially removed.  If  the  observations  should  cover  the 
period  of  a  major  cycle  of  prices,  and  the  commodity 
under  investigation  should  be  a  staple  commodity  such 
as  the  representative  agricultural  products  with  which 
we  shall  have  to  deal,  the  above  method  of  deriving  the 
demand  curve  will  give  an  extremely  accurate  formula 
sunmiarizing  the  relation  between  variations  in  price 


70  Economic  Cycles:  Their  Law  and  Cause 

and  variations  in  the  amount  of  the  commodity  that  is 
demanded. 

The  method  may  be  illustrated  by  deriving  the  law  of 
demand  for  corn.  In  Table  I  of  the  Appendix  to  this 
chapter  are  recorded,  for  the  period  of  1866-1911,  in  the 
United  States,  the  quantities  of  corn  annually  pro- 
duced, the  corresponding  prices  per  bushel,  the  relative 
changes  in  the  quantity  produced  and  the  relative 
changes  in  the  price  per  bushel.  If  the  correlation  of 
the  relative  change  in  the  amount  of  corn  that  is  pro- 
duced and  the  relative  change  in  the  corresponding 
price  per  bushel  of  corn  is  assumed  to  be  hnear,  the 
coefficient  of  correlation  is  r  =  — .789,  and  the  equation 
of  regression  is  ?/  = —.8896.x +7.79,  the  origin  being  at 
{o,o).    (See  Figure  16.) 

In  Tables  ^  II,  III,  IV,  of  the  Appendix  to  this 
chapter,  similar  data  are  given  for  hay,  oats,  and 
potatoes.  The  coefficients  of  correlation  are,  for 
hay,  r  =  —.715;  for  oats,  r  =  —.722;  and  for  potatoes, 
r  =  —.856.    The  regression  equations  are, 

for  hay,  7/ =  — .7643x+3.61; 
for  oats,  ?/  =  — 1.0455a: +6. 93; 
for  potatoes,  ^  =  —1.2194.T  + 15.75; 

the  origin  in  all  cases  being  at  {o^o). 

The  high  coefficients  of  correlation  that  have  just 

been  given  were  obtained  on  the  assumption  that  the 

correlation   between   relative   change   in   amount   de- 

1  The  data  of  the  Tables  I,  II,  III,  IV  were  taken  from  the  Year- 
hook  of  the  Department  of  Agriculture  of  the  United  States,  for 
1911. 


The  Law  of  Demand 


71 


Percentage  chantie  in  the  production   of  corn. 


Figure  16.  The  law  of  demand  for  corn. 
y  =  -.8896x  +  7.79,  origin  at  (0,  0). 


72  Economic  Cycles:  Their  Law  and  Cause 

manded  and  relative  change  in  price  is  linear.  We  shall 
see  later  on  that  the  two  variables  are  even  more 
intimately  associated  than  would  be  suggested  by  the 
high  coefficients  of  correlation.  Just  now  we  wish  to 
know  the  form  of  the  law  of  demand  when  the  restric- 
tion involved  in  the  assumption  of  linearity  of  regres- 
sion is  removed.  What  will  be  the  statistical  laws  of 
demand  for  the  representative  commodities  corn,  hay, 
oats,  and  potatoes,  if  the  regression  of  relative  change  in 
price  upon  relative  change  in  quantity  of  commodity  is 
assumed  to  be  skew  and  of  the  type  y  =a-\-hx-{-cxr-\-dx^1 
The  question  is  answered  by  fitting,  according  to  the 
Method  of  Least  Squares,  the  equation  y  =a+hx-\-cx'^-\r 
dx^  to  the  data  of  Tables  I,  II,  III,  IV  of  the  Appendix 
to  this  chapter.  The  results  of  the  computations  are 
exhibited  in  Figures  17,  18,  19,  20  of  the  text. 

The  statistical  laws  of  demand  for  the  commodities 
corn,  hay,  oats,  and  potatoes  present  the  fundamental 
characteristic  which,  in  the  classical  treatment  of  de- 
mand, has  been  assumed  to  belong  to  all  demand 
curves,  namely,  they  are  all  negatively  inclined ;  that  is 
to  say,  speaking  from  the  point  of  view  of  average 
results,  ''the  greater  the  amount  to  be  sold,  the  smaller 
will  be  the  price  at  which  it  will  find  purchasers,  or,  in 
other  words,  .  .  .  the  amount  demanded  increases 
with  a  fall  in  price  and  diminishes  with  a  rise  in  price."  ^ 

1  Marshall:  Principles  of  Economics,  4th  edit.,  p.  174.  In  case  of 
the  law  of  demand  for  hay,  there  is  a  slight  upward  turn  at  the  ex- 
tremity of  the  curve.  This  is  due  to  one  extreme  observation,  and 
the  variation  is  not  a  significant  exception  to  the  above  general  rule. 


The  Law  of  Demand 


73 


Percenfade  chande   in  the  production   of  corn. 


Figure  17.  The  law  of  demand  for  corn. 
1/  =  .94  —  1.0899a;  +  .0239  1.t  2  —  .000234x3,  origin  at  (0,  0). 


74 


Economic  Cycles:  Their  Law  and  Cause 


1-4S 

\-" 

K 

V- 

h/\ 

\ 

>v.      N 

\ 

^\ 

V 

1 

i 

\ 

^\ 

s; 

\\ 

N 

^ 

A 

\\ 

/\ 

%  -IS 

'^ 

V\ 

^ 

^^ 

) 

-15 

-35 
-AS 

Percenfade   chande   in  the  production  of  hay. 

Figure  18.  The  law  of  demand  for  hay. 
y  =  4.17  —  .9460x  —  .00770x2  +  .OOOSSox',  origin  at  (0,  0). 


The  Law  of  Demand 


75 


^ 


1. 


"^vr — =^, 


Percentage  chande  in   the  production  O'F  oats. 

Figure  19.  The  law  of  demand  for  oats. 
y  =  8.22  —  1.1904X  —  .00663a:»  +  .000273x3,  origin  at  (0,  0). 


76 


Economic  Cycles:  Their  Law  and  Cause 


^^s 

V 


>> 


^" 


V 

\ 

\ 

' 

\k 

f\ 

1 

1 

\ 

V 

\. 

^ 

^^ — s, 

^^ 

K, 

\ 

Percenfade  chende  in  'the  production  of  potatoes. 

Figure  20.  The  law  of  demand  for  potatoes. 
y  =  1.77  —  1.5062X  +  .02489x2—  .000197x^  origin  at  (0,  0). 


The  Law  of  Demand  77 

But  unlike  the  classical  theory  of  demand  which  was 
limited  to  the  simple  enunciation  of  this  one  character- 
istic, coeteris  paribus,  the  statistical  laws  that  have  just 
been  derived  apply  to  the  average  changes  that  society 
is  actually  undergoing.  They  summarize  the  changes 
in  prices  that  are  to  be  expected  from  changes  in  the 
supply  of  the  commodity,  thus  enabUng  one  to  predict 
the  probable  variation  in  price  that  will  follow  upon  an 
assigned  variation  in  the  amount  of  the  commodity. 
They  exhibit  the  connection  of  probable  results  not 
only  in  a  qualitative  but  also  in  a  quantitative  form. 

The  Prediction  of  Prices 

It  has  been  said  that  the  statistical  laws  of  demand 
enable  the  economist  to  predict  the  probable  variation 
in  price  that  will  follow  upon  an  assigned  variation  in 
the  quantity  of  commodity  that  is  to  be  sold.  How 
accurate  are  the  results  of  prediction  that  are  based 
upon  the  statistical  law  of  demand? 

The  accuracy  of  the  prediction  in  the  case  of  any 
given  commodity  will  vary  according  to  the  degree  of 
fit  of  the  type  of  curve  that  is  assumed  to  represent  the 
relation  between  the  relative  change  in  price  and  the 
relative  change  in  the  quantity  of  the  commodity.  If, 
for  example,  the  commodity  in  question  is  corn  in  the 
United  States,  and  the  type  of  demand  curve  is  assumed 
to  be  Unear,  then,  according  to  the  results  in  foregoing 
pages,  the  correlation  between  the  two  variables  is 
r=— .789,  and  the  regression  equation  is  y= — .8896x 
+7.79,  the  origin  being  at  {o,o).     (Figure  16  will  facili- 


78  Economic  Cycles:  Their  Law  and  Cause 

tate  the  discussion  of  the  case.)  By  means  of  this  law 
of  demand  it  is  possible  to  predict  the  probable  change 
in  the  price  that  will  follow  upon  a  given  change  in 
the  quantity  to  be  sold.  In  1911,  in  the  United  States, 
the  quantity  of  corn  produced  was  2,531,488,000 
bushels,  and  the  mean  farm  price  on  December  1,  1911 
was  61.8  cents.  In  1912  the  quantity  of  corn  produced 
was  3,124,746,000  bushels ;  what,  then,  was  the  probable 
price  of  corn  on  December  1,  1912?  The  percentage 
change  in  the  quantity  produced  was  23.44.  Sub- 
stitute this  value  for  x  in  the  formula  for  the  law  of 
demand  y= — .8896a; +7.79,  and  solve  for  the  value 
oiy.  It  is  found  that  the  probable  change  in  price  would 
be  a  fall  of  13.06  per  cent.,  which,  since  the  price  in 
1911  was  61.8  cents,  would  give  52.7  cents  as  the  prob- 
able price  for  December  1,  1912,  whereas  the  actual 
price  was  48.7  cents. 

According  to  the  theory  of  linear  correlation,  the 
accuracy  of  the  regression  equation  as  a  prediction 
formula  is  measured  by  S  =  ^y^  1  —  r-,  where  r  is 
the  coefficient  of  correlation  between  the  variables, 
^y  is  the  standard  deviation  of  the  variable  y  about 
its  mean  value,  and  S  is  the  root-mean-square  devia- 
tion of  the  actual  observations  about  the  regression 
line;  or,  in  other  words,  *S-  is  the  mean  value  of  the 
mean-square  deviations  about  the  regression  line,  of 
the  observations  in  the  several  arrays  of  ?/'s.  From 
the  Table  of  the  Probability  Integral  it  is  known 
that  in  a  symmetrical  distribution  of  observations 
about  their  mean  value,  68  per  cent,  of  all  the  observa- 


The  Law  of  Demand  79 

tions  fall  within  ±  the  root-mean-square  deviation  of 
the  observations  from  their  mean  value;  95  per  cent., 
between  ±  twice  the  root-mean-square  deviation;  and 
99.7  per  cent,  between  =*=  three  times  the  root-mean- 
square  deviation.  It  is  therefore  possible,  by  means 
of  the  Probability  Integral,  to  affix  the  degree  of  prob- 
ability that  a  deviation  shall  fall  within  any  given 
multiples  or  submultiples  of  the  root-mean-square 
deviation.  In  case  of  the  use  of  the  Unear  law  of  de- 
mand for  corn  in  the  United  States  as  a  prediction 
formula,  the  root-mean-square  deviation  of  the  ob- 
servations about  the  demand  curve  was  S  =^y^l—r'^  = 
15.92  per  cent.  That  is  to  say,  if  we  assume  the  law  of 
demand  that  was  based  upon  observations  from  1866 
to  1911  to  hold  in  1912,  then  it  is  95  to  5,  or  19  to  1,  that 
the  percentage  variation  in  the  actual  price  for  1912 
from  the  percentage  variation  as  calculated  from  the 
law  of  demand  will  be  between  ^  2  (15.92),  or  31.84 
per  cent.  The  calculated  percentage  change  in  the 
price  for  1912  was  a  fall  of  13.06  per  cent.;  the  actual 
fall  was  21,20  per  cent.,  giving  a  difference  of  7.14  per 
cent. 

The  precision  with  which  the  linear  law  of  demand 
may  be  used  for  the  prediction  of  the  price  of  corn  in 
the  United  States  justifies  the  belief  that  for  some  pur- 
poses it  is  unnecessary  to  seek  a  greater  degree  of 
accuracy  than  is  afforded  by  the  simple  linear  laws. 
But  it  is  well  to  be  able  to  reach  the  maximum  degree 
of  precision,  and  for  this  reason  we  have  fitted,  to  the 
data  of  the  Tables  in  the  Appendix,  the  more  complex 


80 


Economic  Cycles:  Their  Law  and  Cause 


curves  y  =a-\-bx-\-cx~+dx^,  the  graphs  of  which,  in  case 
of  the  representative  commodities  corn,  hay,  oats,  and 
potatoes,  are  given  in  Figures  17,  18,  19,  20.  What  is 
the  gain  in  precision  when  tlie  more  complex  curve  is 
substituted  for  the  simple  straight  line?  The  scatter 
of  the  observations  about  the  straight  Hne  of  regression 
was  measured,  a  while  ago,  by  taking  the  root-mean- 
square  deviation  of  the  observations  about  the  hne, 
that  is,  by  using  S  =  o'yVl—r'^.  In  order  to  compare 
with  this  result  the  distribution  of  the  observations 
about  the  more  complex  curve,  y  =a-\-hx-\-cx^-\-dx^, 
the  distribution  about  the  latter  curve  will  likewise  be 
measured  by  the  root-mean-square  deviation  of  the 
observations.  In  the  little  table  given  below,  the 
measures  of  scatter  of  the  observations  for  the  two 
types  of  demand  curves  are  presented  in  a  form  that 
will  make  comparison  easy. 


Scatter  of  Observations  About  the  Law  of  Demand 
Root-Mean-Square  Deviation  of  Observations 


Crops 

When  the  regres- 
sion is  linear 

When  the  regres- 
sion is  skew 

Corn 

Hay 

Oats 

Potatoes 

15 .  92  per  cent. 
9.53    "      " 
16.02    "       " 
21.29    "       " 

7 .  36  per  cent. 
4.65    "      " 
10.17    "      " 
9.94    "       '' 

It  is  clear  that  in  all  cases  a  gain  in  precision  is  ob- 
tained by  using  the  more  complex  curve. 

Before  leaving  this  topic  a  remark  should  be  made 


The  Law  of  Demand  81 

that  has  a  bearing  upon  the  a  priori  theory  of  demand. 
In  treatises  on  pure  economics,  particularly  in  those  in 
which  mathematical  analysis  is  employed,  the  masters 
of  the  a  priori  method  point  out  what  they  regard  as 
the  extreme  difficulty  of  the  actual  problem  of  the  rela- 
tion of  price  to  quantity  of  commodity — a  difficulty 
growing  out  of  the  interrelation  of  the  many  factors  in 
the  problem.     If,  to  limit  the  illustration  to  a  simple 
case,  one  wishes  to  know  how  the  price  of  corn  is  re- 
lated to  the  quantity  of  corn  that  is  produced,  he  is 
told  that  the  problem  is  inextricably  complex:  If  there 
is  a  deficiency  in  corn,  then  hay,  or  potatoes,  or  oats, 
or  all  three  may  be  substituted  in  part  for  corn,  and  con- 
sequently the  variation  in  the  price  of  corn  that  fol- 
lows upon  a  deficiency  of  corn  cannot  be  traced  with- 
out knowing  in  what  degree,  when  the  price  of  corn 
varies,  hay,  oats,  and  potatoes  are  used  as  substitutes. 
But  this  is  not  all.    The  degree  in  which  hay,  oats,  and 
potatoes  are  substituted  for  corn  is  dependent  not  only 
upon  the  price  of  corn  but  also  on  their  own  several 
prices,  and  these  latter  prices  are,  in  turn,  dependent 
upon  the  supply   and  price  of  corn!    This  statement  of 
the  problem,  complex  as  it  appears,  is  unduly  simpli- 
fied; and  it  is  presented  not  in  order  to  ridicule  the  work 
of  the  masters  who  have  elaborated  the  method  of 
stating  the  problem  in  the  form  of  simultaneous  equa- 
tions, but  to  show  how  hopelessly  remote  from  reality 
is  the  very  best  theoretical  treatment  of  the  problem 
of  the  relation  of  price  to  the  quantity  of  commodity, 
and  to  suggest,  from  the  results  of  the  preceding  pages 


82  Economic  Cycles:  Their  Law  and  Cause 

of  this  chapter,  how  imaginary,  theoretical  difficulties 
are  dispelled  by  solving  real  problems. 

Of  course  it  is  theoretically  possible  when  there  is  a 
deficiency  in  the  production  of  corn,  that  oats,  hay,  and 
potatoes  may  be  substituted  in  part  for  corn,  but  in- 
stead of  conjuring  up  these  and  other  possibilities  that 
are  never  tested,  would  it  not  be  wise  to  ascertain  first 
just  how  closely  is  the  variation  in  the  price  of  corn 
related  to  the  variation  in  its  own  supply?  When  the 
statistical  investigation  is  made  and  it  is  found  that 
the  correlation  coefficient  is  r  =  — .789,  and  that  when 
a  skew  relation  is  assumed  instead  of  the  usual  linear 
relation,  the  connection  between  the  variables  is  still 
closer,  one  sees  very  clearly,  if  our  illustration  is  a 
typical  case,  that  for  most  of  the  problems  of  actual 
life,  it  is  unnecessary  to  face  the  complex  possible  in- 
terrelation of  phenomena  contemplated  in  the  theoret- 
ical treatment.  For  the  sake  of  economy  of  time  and 
of  talent,  theoretical  and  statistical  work  should  go 
hand  in  hand.  Even  the  complex  theoretical  problem 
that  has  just  been  sketched  may  be  tested  as  to  its 
hypotheses  and  conclusion  by  the  statistical  method 
of  multiple  correlation. 

Elasticity  of  Demand 

The  coefficient  of  the  elasticity  of  demand  for  a 
commodity  has  been  described  as  the  ratio  of  the  rela- 
tive change  in  the  quantity  of  the  commodity  demanded 
to  the  relative  change  in  the  price,  when  the  relative 
changes  are  infinitesimal.     Starting  with  this  descrip- 


The  Law  of  Demand  83 

tion,  we  are  able,  by  means  of  the  laws  of  demand  for 

the  several  commodities,  to  measure  their  respective 

degrees  of  elasticity  of  demand.    It  will  be  recalled  that, 

in  the  form  in  which  the  laws  of  demand  have  been 

presented  in  preceding  pages,  the  variable  x  has  been 

taken  to  represent  the  relative  change  in  the  quantity 

of  the  commodity,  and  the  variable  y,  the  corresponding 

relative  change  in  the  price.     The  coefficient  of  the 

dx 
elasticity  of  demand,  therefore,  is  equal  to  -t-  when  x  is 

zero.  All  that  is  needed  to  obtain  the  measure  of  the 
degree  of  elasticity  of  demand  is  to  differentiate  y  with 
respect  to  x  in  the  equation  to  the  law  of  demand, 
place  x  =  zero,  and  then  take  the  reciprocal  of  the  result. 
The  method  may  be  illustrated  in  case  of  the  four 
representative  commodities,  corn,  hay,  oats,  and  pota- 
toes.   The  law  of  demand  for  corn — see  Figure  17 — is 

y  =  .94-  1.0899X  +  .02391a:2- .000234a:' 

Therefore,  ^  =  -  1.0899  +  2(.02391).c-3(.000234)x2 
ax 

When  a:  =  0,  ^  =  -1.0899,  ^  =-  r74^  =  --92 
dx  dy         1.0899 

and  consequently  the  coefficient  of  the  elasticity  of 

demand  for  corn  is  — .92.    Since  the  law  of  demand  for 

hay  is 

y  =  4. 17-.946:r -.0077x2  +  .000385a:' 

-^  =  —.946  when  x  =  zero, 
dx 

and  the  coefficient  of  elasticity  of  demand  is  — 1.06. 
For  similar  reasons  the  degrees  of  elasticity  of  demand 


84  Economic  Cycles:  Their  Law  and  Cause 

for  oats  and  for  potatoes  are  respectively,  — .84  and 
—.66. 

In  obtaining  these  numerical  values  for  the  coefficient 
of  elasticity,  the  laws  of  demand  for  the  respective 
crops  have  been  assumed  to  be  parabolas  of  the  third 
order.  If  the  linear  laws  of  demand  had  been  taken  for 
the  purpose,  the  coefficients  of  elasticity  would  have 
been    different.     For    example,    the    law    of    demand 

for  corn — see  Figure  16— is  ?/ =— .8896.T  +  7.79    which 

dii  dx 

would  give  -t-= — .8896,  or     t^=— 1.12,  whereas    the 

coefficient  was  — .92  in  case  of  the  more  complex  curve. 
This  discrepancy  between  the  results  when  different 
types  of  curves  are  used  for  the  demand  curve  shows  the 
need  of  care  in  drawing  conclusions  that  are  based  upon 
numerical  values  of  the  coefficient  of  elasticity.  The 
discrepancy  does  not  invalidate  the  method.  When 
different  measures  of  degrees  of  elasticity  are  afforded 
by  different  types  of  curves,  there  is  a  perfectly  satis- 
factory criterion  which  makes  it  possible  to  decide 
between  different  coefficients  of  elasticity:  The  coeffi- 
cient is  to  be  preferred  which  is  deduced  from  the  de- 
mand curve  that  fits  the  data  with  the  highest  degree  of 
probability.  The  demand  curve  that  fits  best  the  data 
affords  the  best  measure  of  the  degree  of  elasticity  of 
demand. 

The  conclusions  of  this  chapter  may  be  briefly  sum- 
marized. In  the  closing  quarter  of  the  last  century 
great  hopes  were  entertained  by  economists  with 
regard  to  the  capacity  of  economics  to  be  made  an 


The  Law  of  Demand  85 

''exact  science."  According  to  the  view  of  the  foremost 
theorists,  the  development  of  the  doctrines  of  utiUty 
and  value  had  laid  the  foundation  of  scientific  economics 
in  exact  concepts,  and  it  would  soon  be  possible  to 
erect  upon  the  new  foundation  a  firm  structure  of 
interrelated  parts  which,  in  definiteness  and  cogency, 
would  be  suggestive  of  the  severe  beauty  of  the 
mathematico-physical  sciences.  But  this  expectation 
has  not  been  realized.  On  the  contrary,  faith  in  the 
possibility  of  an  adequate  ''exact"  treatment  of  the 
science  has  progressively  diminished,  and  interest  in 
economic  theory  m  general  has  decidedly  lost  ground. 
There  must  have  been  somethmg  fundamentally  wrong 
with  the  traditional  handlmg  of  the  subject,  for  cer- 
tainly it  must  be  admitted  that  the  parts  of  a  science 
most  worthy  of  study  are  precisely  those  parts  which  are 
concerned  with  the  general  and  the  universal.  Why, 
then,  should  there  have  been  the  gradual  dissipation  of 
interest  in  theoretical  economics? 

The  explanation  is  found  in  the  prejudiced  point  of 
view  from  which  economists  regarded  the  possibilities  of 
the  science  and  in  the  radically  wrong  method  which 
they  pursued.  It  was  assumed  gratuitously  that 
economics  was  to  be  modeled  on  the  simpler  mathe- 
matical, physical  sciences,  and  this  assumption  created 
a  prejudice  at  the  outset  both  in  selecting  the  data  to  be 
investigated  and  in  conceiving  of  the  types  of  laws  that 
were  to  be  the  object  of  research.  Economics  was 
to  be  a  "calculus  of  pleasure  and  pain,"  a  "mechanics  of 
utility,"  a  "social  mechanics,"  a  ^^ physique  sociale." 


86  Economic  Cycles:  Their  Law  and  Cause 

The  biased  point  of  view  implied  in  these  descriptions 
led  to  an  undue  stressing  of  those  aspects  of  the  science 
which  seemed  to  bear  out  the  pretentious  metaphors. 
One  would  naturally  suppose  from  this  manner  of 
conceiving  the  science  that  the  economic  theorists 
would  at  once  have  entered  upon  their  task  with  the 
methods  that  had  proved  themselves  useful  in  the 
physical  sciences.  But  this  they  did  not  do.  They 
seemed  to  identify  the  method  of  physical  sciences  with 
experimentation,  and  since,  as  they  held,  scientific 
experimentation  is  impossible  in  social  life,  a  special 
method  had  to  be  devised.  The  invention  was  a  dis- 
guised form  of  the  classical  cceteris  paribus,  the  method 
of  the  static  state. 

The  point  of  view  that  has  been  exemplified  in  this 
chapter  is  that  the  facts  in  their  full  concreteness  must 
never  be  lost  from  sight ;  that  the  laws  which  are  sought 
are  of  necessity,  at  first,  proximate  laws,  laws  that 
obtain  in  full  empirical  reality,  and  are  means  of  arriv- 
ing at  laws  of  larger  generality;  that  the  method  to  be 
followed  is  the  method  which  makes  progress  from  the 
data  to  generalization  by  a  progressive  synthesis — 
the  method  of  statistics.^ 

1  With  regard  to  the  methodology  of  the  social  sciences,  the 
writings  of  Cournot  are  always  hclj^ful.  The  following  quotatipn 
is  taken  from  a  treatise  published  thirteen  years  after  his  epoch 
making  Recherches  sur  les  principes  matMmatiques  de  la  theorie  des 
richesses. 

Si  nous  restons  dans  I'ordre  des  causes  secondaires  et  des  faits 
observables,  le  seul  auquel  la  science  puisse  atteindre,  la  theorie 
math^matique  du  hasard  .  .  .  nous  apparait  comme  I'apphcation 
la  plus  vaste  de  la  science  des  nombres,  et  celle  qui  justifie  le  mieux 


The  Law  of  Demand  87 

Starting  with  this  point  of  view  and  pursuing  the 
method  that  has  just  been  described,  we  have  attacked 
the  old  problem  of  the  form  of  the  law  of  demand.  We 
have  obtained  the  concrete  laws  of  demand  for  repre- 
sentative commodities,  have  affixed  the  degree  of  preci- 
sion with  which  the  laws  may  be  used  as  formulae  for 
predicting  prices,  and  have  measured  the  elasticity  of 
demand  for  the  respective  commodities. 

In  all  likelihood  it  will  be  said  that  what  we  have 
achieved  is  not  exactly  what  the  partisans  of  the  method 
of  cceteris  paribus  proposed.  To  this  criticism  we  reply 
that  their  immediate  problem  of  the  relation  of  price  and 
quantity  of  commodity,  cceteris  paribus,  was  vaguely 
conceived  and  actually  abandoned  by  those  who  sought 
to  give  it  definiteness,  as  being  incapable  of  concrete 

I'adage:  Mundum  regunt  numeri.  En  cffet,  quoiqu'en  aient  pens6 
certains  philosophes,  rien  ne  nous  autorise  a  croire  qu'on  puisse 
rendre  raison  de  tous  les  phenomencs  avcc  les  notions  d'etenduc,  de 
temps,  de  mouvement,  en  un  mot,  avec  les  seules  notions  des  grand- 
eurs continues  sur  lesquelles  portent  les  mesures  et  les  calculs  du 
g^ometre.  Les  actes  des  etres  vivants,  intelligents  et  moraux  ne 
s'expliquent  nuUement,  dans  I'etat  de  nos  connaissances,  et  11  y  a 
de  bonnes  raisons  de  croire  qu'ils  ne  s'expliqueront  jamais  par  la 
mecanique  et  la  geom^trie.  lis  ne  tombent  done  point,  ]!ar  le  cote 
g^om^trique  ou  mecanique  dans  le  domaine  des  nombres,  niais  ils 
s'y  retrouvcnt  places,  en  tant  que  les  notions  de  combinaison  et  de 
chance,  de  cause  et  de  hasard,  sont  superieures,  dans  I'ordre  des 
abstractions,  S,  la  geometric  et  k  la  mecanique,  et  s'appliquent  aux 
ph^nomenes  de  la  nature  vivante  comme  k  ceux  que  produisent  les 
forces  qui  sollicitent  la  mati^rc  inorganiquc;  aux  actes  r^flechis  des 
6tres  libres,  comme  aux  determinations  fatales  de  I'app^tit  et  de 
I'instinct. 

Essai  sur  les  fondements  de  nns  connaissances  et  sur  les  caracteres 
de  la  critique  philosophiqne,  vol.   1,  pp.   64-65. 


88  Economic  Cyces:  Th  eir  Law  and  Cause 

solution;  that  when  the  problem  is  clearly  stated,  it 
admits  of  solution  by  means  of  a  method  which  we  have 
indicated,  the  method  of  multiple  correlation;  and  that 
what  we  have  achieved  is  the  solution  of  their  ultimate 
problem  of  the  relation  of  price  and  quantity  of  com- 
modity in  a  dynamic  society. 


.\PPENDIX 


TABLE  I. — The  Production  and  the  Price  of  Corn  in  the 
United  States 


Average 

Production  of 

Farm  Price 

Percentage 

Percentage 

Year 

Corn  in  Thou- 

Per Bushel 

Change  in 

Change  in 

sands  OF  Bushels 

December  1, 
IN  Cents 

Production 

Price 

1866 

867,946 

47.4 

1867 

768,320 

57.0 

—11.48 

+  19.41 

1868 

906,527 

46.8 

+  17.99 

—17.89 

1869 

874,320 

59.8 

—  3.55 

+27.78 

1870 

1,094,255 

49.4 

+25.15 

—17.39 

1871 

991,898 

43.4 

—  9.35 

—12.15 

1872 

1,092,719 

35.3 

+  10.17 

—18.66 

1873 

932,274 

44.2 

—14.68 

+25.21 

1874 

850,148 

58.4 

—  8.81 

+32.13 

1875 

1,321,069 

36.7 

+55.39 

—37.16 

1876 

1,283,828 

34.0 

—  2.82 

—  7.36 

1877 

1,342,558 

34.8 

+  4.57 

+  2.35 

1878 

1,388,219 

31.7 

+  3.40 

—  8.91 

1879 

1,547,902 

37.5 

+  11.50 

+  18.30 

1880 

1,717,435 

39.6 

+  10.95 

+  5.60 

1881 

1,194,916 

63.6 

—30.42 

+60.61 

1882 

1,617,025 

48.5 

+35.33 

—23.74 

1883 

1,551,067 

42.4 

—  4.08 

—12.58 

1884 

1,795,528 

35.7 

+  15.76 

—15.80 

1885 

1,936,176 

32.8 

+  7.83 

—  8.12 

1886 

1,665,441 

36.6 

—13.98 

+  11.59 

1887 

1,456,161 

44.4 

—12.57 

+21.31 

1888 

1,987,790 

34.1 

+36.51 

—23.20 

1889 

2,112,892 

28.3 

+  6.29 

—17.01 

1890 

1,489,970 

50.6 

—29.48 

+78.80 

1891 

2,060,154 

40.6 

+38.27 

—19.76 

1892 

1,628,464 

39.4 

—20.95 

—  2.96 

1893 

1,619,496 

36.5 

—     .55 

—  7.36 

1894 

1,212,770 

45.7 

—25.11 

+25.21 

1895 

2,151,139 

25.3 

+77.37 

—44.64 

1896 

2,283,875 

21.5 

+  6.17 

—15.02 

1897 

1,902,968 

26.3 

-16.68 

+22.33 

1898 

1,924,185 

28.7 

+  1.11 

+  9.13 

1899 

2,078,144 

30.3 

+  8.00 

+  5.57 

1900 

2,105,103 

35.7 

+  1.30 

+  17.82 

1901 

1,522,520 

60.5 

—27.67 

+69.47 

1902 

2,523,648 

40.3 

+65.75 

—33.39 

1903 

2,244,177 

42.5 

—11.07 

+  5.46 

1904 

2,467,481 

44.1 

+  9.95 

+  3.76 

1905 

2,707,994 

41.2 

+  9.75 

—  6.58 

1906 

2,927,416 

39.9 

+  8.10 

—  3.16 

1907 

2,592,320 

51.6 

—11.45 

+29.32 

1908 

2,668,651 

60.6 

+  2.94 

+  17.44 

1909 

2,772,376 

59.6 

+  3.89 

—  1.65 

1910 

2,886,260 

48.0 

+  4.11 

—19.46 

1911 

2,531,488 

61.8 

—12.29 

+28.75 

89 


90 


Economic  Cycles:  Their  Law  and  Cause 


TABLE  II. — The  Production  and  the  Price  of  Hay  in  the 
United  States 


Year 

Production  of 
Hay  in  Thou- 
sands OF  Tons 
(Ton  =  2000  Ibs.l 

Average   Farm, 

Prick  Per  Ton 

December  1, 

IN  Dollars 

Percentage 
C'hangf.  in 
Production 

Percentage 

Change  in 

Price 

1866 

21,779 

10.14 

1867 

26,277 

10.21 

+20.65 

+     .69 

1868 

26,142 

10.08 

—  2.42 

—  1.27 

1869 

26,420 

10.18 

+  1.06 

+     .99 

1870 

24,525 

12.47 

—  7.17 

+22 .  50 

1871 

22,239 

14.30 

—  9.32 

+  14.68 

1872 

23,813 

12.94 

+  7.08 

—  9.51 

1873 

25,085 

12.53 

+  5.34 

—  3.17 

1874 

25,134 

11.94 

+      .20 

—  4.71 

1875 

27,874 

10.78 

+  10.90 

—  9.72 

1876 

30,867 

8.97 

+  10.74 

—16.79 

1S77 

31,629 

8.37 

+  2.47 

—  6.69 

1878 

39,608 

7.20 

+25.23 

—13.98 

1879 

35,493 

9.32 

—10.39 

+29.44 

1880 

31,925 

11.65 

—10.05 

+25.00 

1881 

35,135 

11.82 

+  10.05 

+  1.46 

1882 

38,138 

9.73 

+  8.55 

—17.68 

1883 

46,864 

8.19 

+22.88 

—15.83 

1884 

48,470 

8.17 

+  3.43 

—     .24 

1885 

44,732 

8.71 

—  7.71 

+  6.61 

1886 

41,796 

8.46 

—  6.56 

—  2.87 

1887 

41,454 

9.97 

—     .82 

+  17.86 

1888 

46,643 

8.76 

+  12,52 

—12.14 

1889 

66,831 

7.04 

+43,27 

—19.63 

1890 

60,198 

7.87 

—  9 ,  93 

+  11.79 

1891 

60,818 

8.12 

+  1,03 

+  3.18 

1892 

59,824 

8.20 

—  1,63 

+      .99 

1893 

65,766 

8.68 

+  9,93 

+  5.85 

1894 

54,874 

8.54 

—16,56 

—  1.61 

1895 

47,079 

8.35 

—14.21 

—  2.22 

1896 

59,282 

6.55 

+25.92 

—21.56 

1897 

60,665 

6.62 

+  2,33 

+  1.07 

1898 

66,377 

6.00 

+  9,42 

—  9.37 

1899 

56,656 

7.27 

—14,65 

+21.17 

1900 

50,111 

8.89 

—11,55 

+22.28 

1901 

50,591 

10.01 

+      .96 

+  12.60 

1902 

59,858 

9.06 

+  18.32 

—  9.50 

1       1903 

61,306 

9.07 

+  2.42 

+      .11 

i       1904 

60,696 

8.72 

—  1.00 

—  3.86 

1905 

60,532 

8.52 

—     .27 

—  2.29 

I       1906 

57,146 

10.37 

—  5.59 

+21.71 

[       1907 

63,677 

11.68 

+  11.43 

+  12.63 

i       1908 

70,798 

8.98 

+  11.18 

—23.12 

1909 

64,938 

10.62 

—  8.28 

+  18.26 

1910 

60,978 

12,26 

—  6,10 

+  15.44 

1911 

47,444 

14.64 

—22.19 

+  19.41 

The  Law  of  Demand 


91 


TABLE  III. — The  Production  and  the  Price  of  Oats  in  the 
United  States 


Average 

Production  op 

Farm  Price 

Percentage 

Percentage 

Year 

Oats  in  Thod- 

Per  Bushel 

Change  in 

Change  in 

SANDs  OF  Bushels 

December  1, 
IN  Cent8 

Production 

Price 

1866 

268,141 

35.1 

1867 

278,698 

44.5 

+  3.94 

+26.78 

1868 

254,961 

41.7 

—  8.52 

—  6.29 

1869 

288,334 

38.0 

+  13.09 

—  8.87 

1870 

247,277 

39.0 

—14.24 

+  2.63 

1871 

255,743 

36.2 

+  3.42 

—  9.66 

1872 

271,747 

29.9 

+  6.26 

—17.40 

1873 

270,340 

34.6 

—     .52 

+  15.72 

1874 

240,369 

47.1 

—11.09 

+36.13 

1875 

354,318 

32.0 

+47.41 

—32.06 

1876 

320,884 

32.4 

—  9.44 

+  1.25 

1877 

406,394 

28.4 

+26.65 

—12.35 

1878 

413,579 

24.6 

+  1.77 

—13.38 

1879 

363,761 

33.1 

—12.05 

+34.55 

1880 

417,885 

36.0 

+  14.88 

+  8.76 

1881 

416,481 

46.4 

—     .34 

+28.89 

1882 

488,251 

37.5 

+  12.43 

—19.18 

1883 

571,302 

32.7 

+  17.01 

—12.80 

1884 

583,628 

27.7 

+  2.16 

—15.29 

1885 

629,409 

28.5 

+  7.84 

+  2.89 

1886 

624,134 

29.8 

—     .84 

+  4.56 

1887 

659,618 

30.4 

+  5.68 

+  2.01 

1888 

701,735 

27.8 

+  6.39 

—  8.55 

1889 

751,515 

22.9 

+  7.09 

—17.63 

1830 

523,621 

42.4 

—30.32 

+85.15 

1891 

738,394 

31.5 

+41.02 

—25.71 

1892 

661,035 

31.7 

—10.48 

+      .63 

1893 

638,855 

29.4 

—  3.36 

—  7.26 

1894 

662,037 

32.4 

+  3,63 

+  10.20 

1895 

824,444 

19.9 

+24.53 

—38.58 

1896 

707,346 

18.7 

—14.20 

—  6.03 

1897      1 

698,768 

21.2 

—  1.21 

+  13.37 

1898      ' 

730,907 

25.5 

+  4.60 

+20.28 

1899 

796,178 

24.9 

+  8.93 

—  2.35 

1900      I 

809,126 

25.8 

+  1.63 

+  3.61 

1901 

736,809 

39.9 

—  8  94 

+54.65 

1902 

987,843 

30.7 

+34.07 

—23.06 

1903 

784,094 

34.1 

—20.52 

+  11.07 

1904      ' 

894,596 

31.3 

+  14.09 

—  8.21 

1905 

953,216 

29.1 

+  6.55 

—  7.03 

1903 

964,905 

31.7 

+  1.23 

+  8.93 

1907 

754,443 

44.3 

—21.81 

+39.75 

1908      1 

807,156 

47.2 

+  6.99 

+  6.55 

1909 

1,(K)7,353 

40.5 

+24.80 

—14.19 

1910 

1,186,341 

34.4 

+  17.77 

—15.06 

1911 

922,298 

45.0 

—22.26 

+30.81 

92 


Economic  Cycles:  Their  Law  and  Cause 


TABLE  IV. — The  Production  and  the  Price  of  Potatoes  in 
THE  United  States 


Production  of 
pot.\toes  in 

AVER.\QB 

Farm  Price 

Percentage 

Percentage 

Year 

Per  Bushel 

Change  in 

Change  in 

Thous.\.nd.s  OF 

December  1, 

Production 

Price 

Bushels 

IN  Cents      I 

1866 

107,201 

47.3 

1867 

97,783 

65.9 

—  8.79 

+39.32 

1868 

106,090 

59.3 

+  8.50 

—10.02 

1869 

133,886 

42.9 

+26.20 

—27.66 

1870 

114,775 

65.0 

—14.27 

+51.52 

1871 

120,462 

53.9 

+  4.95 

—17.08 

1872 

113,516 

53.5 

—  5.77 

—     .74 

1873 

106,089 

65.2 

—  6.54 

+21.87 

1874 

105,981 

61.5 

—     .10 

—  5.67 

1875 

166,877 

34.4 

+57.46 

—44.07 

1876 

124,827 

61.9 

—25.20 

+79.94 

1877 

170,092 

43.7 

+36.26 

—29.40 

1878 

124,127 

58.7 

—27.02 

+34.32 

1879 

181,626 

43.6 

+46.32 

—25.72 

1880 

167,660 

48.3 

—  7.69 

+  10.78 

1881 

109,145 

91.0 

—34.90 

+88.41 

1882 

170,973 

55.7 

+56.65 

—38.79 

1883 

208,164 

42.2 

+21.75 

—24.24 

1884 

190,642 

39.6 

—  8.42 

—  6.16 

1885 

175,029 

44.7 

—  8.19 

+  12.88 

1886 

168,051 

46.7 

—  3.99 

+  4.47 

1887 

134,103 

68.2 

—20.20 

+46.04 

1888 

202,365 

40.2 

+50.90 

—41.06 

1889 

204,881 

35.4 

+   1.24 

—11.94 

1890 

148,290 

75.8 

—27.62 

+  114.12 

1891 

254,424 

35.8 

+71.57 

—52 .  77 

1892 

156,655 

66.1 

—38.43 

+84.64 

1893 

183,034 

59.4 

+  16.84 

—10,14 

1894 

170,787 

53.6 

—  6.69 

—  9.76 

1895 

297,237 

26.6 

+74.04 

—50.37 

1896 

252,235 

28.6 

—15.14 

+  7.52 

1897 

164,016 

54.7 

—34.97 

+91.26 

1898 

192,306 

41.4 

+  17.25 

—24.31 

1899 

228,783 

39.0 

+  18.97 

—  5.80 

1900 

210,927 

43.1 

—  7.80 

+  10.51 

1901 

187,598 

76.7 

—11.06 

+77.96 

1902 

284,633 

47.1 

+51.72 

—38.59 

1903 

247,128 

61.4 

—13 .  18 

+30.36 

1904 

332,830 

45.3 

+34.68 

—26 .  22 

1905 

260,741 

61.7 

—21.66 

+36.20 

1906 

308,038 

51.1 

+  18.14 

—17.18 

1907 

298,262 

61.8 

—  3.17 

+20.94 

1908 

278,985 

70.6 

—  6.46 

+  14.24 

1909 

376,537 

54.9 

+34.97 

— 22  24 

1910 

349,032 

55.7 

—  7.30 

+   1^46 

1911 

292,737 

79.9 

—16.13 

+43.45 

CHAPTER  V 

THE  MECHANISM   OF  CYCLES 

"Agriculture  is  the  Foundation  of  Manufacture  and  Commerce." 
— Motto  of  the  United  States  Department  of  Agriculture. 

Thus  far  in  our  investigation  of  the  cause  and  law  of 
economic  cycles,  we  have  shown  that  the  annual  rainfall 
in  the  principal  grain-producing  area  of  the  United 
States  passes  through  definite,  well-defined  cycles;  and 
that  the  yield  of  typical,  leading  crops  is  so  closely 
related  to  the  rainfall  of  their  respective  critical  seasons 
that  the  cyclical  movement  of  the  rainfall  of  the  critical 
seasons  is  approxmiately  reproduced  in  the  yield  per 
acre  of  the  corresponding  crops.  These  cycles  of  crops 
constitute  the  natural,  material  current  which  drags 
upon  its  surface  the  lagging,  rhythmically  changing 
values  and  prices  with  which  the  economist  is  more 
immediately  concerned.  In  order  to  understand  the 
connection  between  the  flow  of  the  undercurrent  of 
agricultural  yield  and  the  surface  changes  of  values  and 
prices,  we  have  taken  the  necessary  first  step  of  con- 
necting the  prices  of  agricultural  commodities  with 
their  supply.  But  the  supply  varies  with  the  acreage  as 
well  as  with  the  yield,  and  consequently  to  carry  further 
our  investigation  we  must  know  how  closely  the  prices 
of  crops  are  related  to  their  yield. 

93 


94  Economic  Cycles:  Their  Law  and  Cause 

The  Prices  of  Agricultural  Commodities  Correlated  with 
the  Yield  of  the  Several  Crops 

The  method  employed  in  the  preceding  chapter  to 
derive  the  law  of  demand  of  the  several  crops  contained 
two  stages:  As  a  first  stage,  the  correlation  between  the 
relative  change  in  the  total  supply  and  the  correspond- 
ing relative  change  in  price  was  assumed  to  be  linear, 
and  upon  the  hypothesis  of  linearity  of  regression,  the 
demand  curve  was  computed  and  the  degree  of  accuracy 
with  which  prices  might  be  predicted  from  such  linear 
demand  curves  we  showed  how  to  measure.  The  second 
stage  in  the  theory  of  demand  curves  was  to  assume  a 
skew  relation  between  relative  changes  in  price  and 
supply,  and  we  found  that  the  degree  of  accuracy  with 
which  prices  might  be  predicted  from  the  skew  demand 
curves  was  greater  than  when  the  law  of  demand  was 
assumed  to  be  linear.  We  shall  follow  these  two  stages 
in  treating  the  relation  between  the  yield  per  acre  and 
the  price  of  the  crops. 

If  the  correlation  between  the  relative  change  in 
yield  per  acre  and  the  relative  change  in  price  is  as- 
sumed to  be  linear,  we  obtain  for  the  coefficients  of 
correlation  in  case  of  the  four  typical  crops,  the  values 
placed  in  the  first  row  of  the  accompanying  Table, 
which,  for  purpose  of  comparison,  also  presents  the 
corresponding  coefficients  in  case  of  the  linear  demand 
curves. 


The  Mechanism  of  Cycles 


95 


A  Comparison  of  the  Coefficients  of  Correlation  in 
Case  of  Linear  Yield-Price  Curves  and  of  Linear 
Demand  Curves 


Corn 

Hay 

Oats 

Potatoes 

Relative    change    in 
yield  per  acre  and 
relative  change  in 
price 

—  .815 

—  .656 

—  .718 

—  .873 

Relative    change    in 
total    supply    and 
relative  change  in 
price 

—  .789 

—  .715 

—  .722 

—  .856 

J 

The  data  used  in  the  above  computation  were,  in 
case  of  the  yield-price  curve,  the  average  yield  per  acre 
of  the  respective  crops  in  the  whole  of  the  United 
States  and  the  corresponding  average  prices  for  the 
United  States,  on  the  first  of  December  of  the  years  in 
which  the  crops  were  produced.  The  data  for  the 
demand  curves,  it  will  be  recalled  from  the  preceding 
chapter,  were  the  total  supply  of  the  respective  crops 
in  the  United  States  and  the  corresponding  prices  on 
December  1.  The  period  covered  in  both  cases  was 
from  1866  to  1911,  inclusively.  The  data  were  ob- 
tained from  recent  Yearbooks  of  the  United  States 
Department  of  Agriculture. 

It  appears,  from  the  coefficients  of  correlation  given 
in  the  above  Table,  that  it  is  possible  to  predict  the 
prices  of  the  crops  from  the  yield  per  acre  with  the  same 


96  Economic  Cycles:  Their  Law  and  Cause 

precision  with  which  prices  may  be  predicted  from  the 
demand  curves.  Or,  to  put  the  idea  in  another  form, 
the  productivity  of  the  soil  is  as  closely  related  to  the 
prices  of  crops  as  the  supply  of  the  commodity  is  related 
to  the  same  prices.  In  the  chapter  on  the  ''Law  of 
Demand,"  we  found  that,  when  the  relative  change  in 
the  supply  is  given,  the  mean  shift  in  the  corresponding 
change  of  price  may  be  obtained  from  the  regression 
equation,  and  that,  furthermore,  the  root-mean-square 
deviation  of  the  observations  may  be  computed  by 
the  formula  S  =^y^l—r''.  This  same  formula  may 
be  used  for  a  similar  purpose  in  case  of  the  yield-price 
curves. 

We  come  now  to  the  second  stage  in  the  derivation  of 
the  relation  between  price  and  the  yield  per  acre  of 
crops.  We  assume  that  the  relation  between  the  yield 
per  acre  and  the  price  of  a  crop  is  skew,  and  that  the 
relation  between  the  two  may  be  expressed  by  an 
equation  of  the  form  y  =a+bx-{-cx'^-{-dx^. 

In  Figure  21,  the  skew  yield-price  curves  of  our  four 
representative  commodities  are  drawn  to  a  percentage 
scale.  The  equations  to  the  curves,  which  were  com- 
puted by  the  Method  of  Least  Squares,  are  given  upon 
the  Figure.  The  root-mean-square  deviation  of  the 
observations  from  their  respective  yield-price  curves 
are  given  in  the  following  Table  which,  for  purposes 
of  comparison,  reproduces  the  coefficients  that  were 
found,  in  the  preceding  chapter,  to  measure  the  devia- 
tion of  the  observations  about  the  skew  laws  of  de- 
mand. 


The  Mechanism  of  Cycles 


97 


i^65 


\^Si 


^ 


Percenfgde  chgnde  in  the  yie/ii  per  acre  of  corn       Percer^fsde  chande  /n  the  yie/d  per  acre   of  hay. 


Percenfijde  chdnie  in  the  yield  per  sere  ofosfs      Percentdde  chande  in  the  yield  per  acre  ofpotafdes 


Figure  21.  The  relation  between  the  price  and  the  yield  per  acre  of  the 

several  crops. 
When  the  origin  is  at  (0,  0),  the  equations  are 

For  corn,  y  =  .17  —  1.2989.r  +  .01892.c2  —  .000137.c3. 
For  hay,  y  =  1.17  —  1.0215x  +  .01549.c2  +  .00009.r3. 
For  oats,  y  =  —  1.49  —  1.1346x  +  .02324x2  —  .000238x3. 
For  potatoes,  i/  =  .49  —  1.4863x  +  .01993x2  —  .000141x^ 


98  Economic  Cycles:  Their  Law  and  Cause 


A  Comparison  of  the  Root-Mean-Square  Deviation  in 
Case  of  Skew  Yield-Price  Curves  and  of  Skew  De- 
mand Curves 


Corn 

Hay 

Oats 

Potatoes 

Yield-Price 
Curves 

5.48 

5.72 

7.05 

9.39 

Demand 

Curves 

7.36 

4.65 

10.17 

9.94 

From  the  results  given  in  the  last  two  Tables,  it  is  clear 
that  the  prices  of  the  representative  crops  are  as  closely 
related  to  the  yield  per  acre  as  to  the  total  supply  of  the 
crops.  This  conclusion  is  of  importance  in  the  task  of 
connecting  the  cycles  in  the  productivity  of  the  soil  with 
the  cycles  in  values  and  prices. 

In  obtaining  the  preceding  close  relations  between  the 
changes  in  prices  and  changes  in  yield,  the  figures  for  the 
whole  of  the  United  States  were  employed.  The  object 
of  broadening  the  field  of  observation  from  the  detailed 
investigation  of  the  Middle  West  to  the  whole  of  the 
United  States  was  two-fold:  First,  it  seemed  likely,  a 
priori,  that  a  more  intimate  relation  between  prices  and 
yield  would  be  obtained  if  the  large  market  of  the  whole 
country  were  substituted  for  the  local  market  of  Ilhnois; 
secondly,  because  the  object  of  this  chapter  is  to  bring 
the  physical  cycles  of  crops  into  relation  with  the 
industrial  and  commercial  changes  of  the  whole  country, 
and  to  this  end  it  seemed  desirable  that  the  crops  of  the 


The  Mechanis7n  of  Cycles  99 

whole  country  should  be  considered.  We  need,  how- 
ever, to  assure  ourselves  that,  in  taking  this  more 
comprehensive  view  of  the  yield  of  crops,  we  have  not 
lost  the  characteristic  cyclical  movement  of  the  yield 
which  we  discovered  in  the  more  limited  study.  We 
desire  to  know  how  closely  the  yield  per  acre  of  the 
whole  country  is  correlated  with  the  yield  per  acre  of 
our  representative  state  of  Illinois. 

The  correlations  of  the  annual  differences  in  the  yield 
per  acre  in  Illinois  and  the  annual  differences  in  the 
yield  per  acre  in  the  United  States  were,  in  case  of  our 
four  typical  crops,  for  corn,  r  =  .855;  for  hay,  r  =  .745; 
for  oats,  r  =  .800;  for  potatoes,  r  =  ,843.  The  period 
covered  in  all  cases  was  from  1866  to  1912  inclusively. 
The  data  were  obtained  from  Bulletins,  56,  58,  62,  63 
of  the  Bureau  of  Statistics  of  the  United  States  Depart- 
ment of  Agriculture  and  from  the  recent  Yearbooks  of 
the  same  Department.  A  reference  to  the  Table  given 
a  moment  ago  will  show  that  the  yield  per  acre  of  crops 
in  Illinois  is  at  least  as  closely  related  to  the  yield  per 
acre  of  the  same  crops  in  the  United  States,  as  the  prices 
of  the  several  crops  are  related  either  to  the  supply 
of  the  crops  or  to  the  yield  per  acre  of  the  crops.  More- 
over, the  very  high  values  of  the  coefficients  leave  but 
little  room  for  doubt  that  the  cyclical  movement  of  the 
yield  per  acre  in  the  Middle  West  is  representative  of 
the  movement  of  the  crop  yield  in  the  whole  of  the 
United  States. 


100         Economic  Cycles:  Their  Law  and  Cause 

Rising  and  Falling  Prices   as  Related   to    Yield-Price 

Curves 

Thus  far  it  is  clear  that  the  prediction  of  agricul- 
tural prices  is  dependent  upon  a  knowledge  (1)  of  the 
law  of  the  variations  of  price  with  the  yield  per  acre, 
and  (2)  of  the  law  of  the  annual  change  in  the  yield  per 
acre  of  the  several  crops.  If  the  relation  between  prices 
and  yield  per  acre  were  constant,  the  theory  of  agricul- 
tural cycles  would  be  completely  elucidated;  for,  once 
having  discovered  the  law  of  the  relation  of  price  to 
yield  per  acre,  nothing  more  would  be  necessary  then 
to  connect  the  yield  with  the  meteorological  conditions 
of  its  critical  season,  and  the  resulting  prices  for  a  long 
term  of  years  could  be  predicted  with  great  probabihty. 
But  the  relation  between  the  price  of  the  crops  and  the 
yield  per  acre  varies  with  the  level  of  general  prices,  and 
it  is  of  the  first  importance  to  know  the  manner  of  varia- 
tion. 

If  the  course  of  prices  in  the  United  States  for  the 
period  1866  to  1911  is  examined,  it  w411  be  seen  that, 
in  general  terms,  we  may  with  justness  characterize  the 
period  1866  to  1890  as  a  period  of  falling  prices,  and  the 
period  1890  to  1911  as  a  period  of  rising  prices.  If 
therefore,  in  case  of  each  of  our  representative  com- 
modities, we  construct  two  yield-price  curves,  one 
for  the  period  of  falling  prices  and  one  for  the  pe- 
riod of  rising  prices,  we  shall,  by  comparing  the  two 
curves  for  the  two  periods,  discover  how  the  demand 
curves,  or  yield-price  curves,  vary  in  periods  in  which 


The  Mechanism  of  Cycles  101 

the  movement  of  general  prices  is  in  opposite  direc- 
tions. 

In  Figure  22,  the  eight  curves  are  drawn.  Compar- 
ing the  curves  in  the  two  periods  for  each  of  the  four 
representative  crops  we  infer  that 

(1)  the  demand  schedule  or  yield-price  curve  is  high 

when  the  general  level  of  prices  is  high;  and 
the  demand  schedule  is  low  when  the  general 
level  of  prices  is  low; 

(2)  the  general  run  of  the  curves  remains  nearly  the 

same.  That  is  to  say,  the  principal  difference 
between  the  period  of  falling  prices  and  period 
of  rising  prices  is  that  the  yield-price  schedules 
move  down  or  up. 

These  are  general  statements  in  which  quite  obvious 
deviations  are  ignored  and  which,  consequently,  do 
not  pretend  to  quantitative  accuracy.  The  construc- 
tion of  the  curves  is  dependent  upon  too  few  observa- 
tions to  admit  of  attaching  significance  to  the  apparent 
exceptions  to  the  rule. 

Since  the  prices  of  the  representative  crops  are,  as  we 
know,  dependent  upon  the  yield  per  acre  and  the  law 
of  the  relation  between  prices  and  the  yield  per  acre, 
and  since,  as  we  have  proved,  the  yield-price  curves 
move  with  the  general  level  of  prices,  our  desideratum 
is  to  discover  what  determines  the  change  in  the  level 
of  general  prices. 


102         Economic  Cycles:  Their  Law  and  Cause 


Percenf-d^e  chande  in  iheyieJd per  acre  afoafs       ^ercenfs^e  chanSe  in  the  yield  per  acre  ofpofdfbes. 


Figure  22.  The  relation  between  the  price  and  the  yield  per  acr; 

several  crops. 
When  the  origin  is  at  {0,0),  the  equations  are 


of  the 


For  corn 


For  hay 


For  oats 


For  potatoes 


yrs.  1866-1889,  _ ._,  i/=— 2.00— 1.0299x  +  .01926x2— .000312.r3. 

yrs.  1890-1911, ,  xj  =      3.06— 1.4894x  +  .01737j-2^.000049.r3. 

yrs.  1866-1889,  -    _,  ?/  =  — 5.72— 1.6435x  +  . 07798x2— .000574j-'. 

yrs.  1890-1911, ,y=     5.41—  .7306x— .00591.r2+.000075x^ 

yrs.  1866-1889, ?/  =  — 2.78— 1.6039x— .00546j-2  +  .0OO778x». 

yrs.  1890-191 1,  — ,  y  =  .99— 1.0240x  +  . 02394x2— .000383x3. 
yrs.  1866-1889,  _,  ?/  =  - 3.92— 1.4424x  +  .01684x2— .000020x». 
yrs.  1890-1911, ,2/  =  —  .91— 1.6068x  +  .03831x2— .000397x». 


The  Mechanism  of  Cycles  1 03 

The  Volume  of  Crops  and  the  Activity  of  Industry 

We  shall  approach  the  problem  of  the  cause  of  the 
changing  level  of  prices  by  considering  two  preliminary 
questions  which  will  enter  into  the  subsequent  argu- 
ment: (1)  Is  there  any  relation  between  the  changing 
volume  of  the  crops  and  the  changing  volume  of  those 
producers'  goods  whose  fluctuations  are  generally  re- 
garded as  indices  of  the  activity  of  trade?  (2)  Is  the 
law  of  demand  for  crops  the  type  of  law  that  is  repro- 
duced in  the  demand  for  all  commodities,  or  is  it  not 
rather  the  case  that  the  law  of  demand  for  pure  pro- 
ducers' goods  is  of  a  different  type  from  the  law  of 
demand  for  those  commodities  of  which  our  four  crops 
are  samples? 

The  first  of  these  two  questions  we  shall  consider  in  a 
form  modified  to  bring  its  significance  to  bear  upon  the 
results  that  have  already  been  established.  The  volume 
of  crops  varies  with  the  extent  of  the  acreage  and  with 
the  average  yield  per  acre.  The  question  of  interest 
to  us  at  this  point  is  whether  the  volume  of  producers' 
goods  fluctuates  with  the  yield  per  acre  of  the  crops. 
We  shall  investigate  this  question,  and,  as  a  means  of 
carrying  forward  our  inquiry,  we  first  construct  an 
index  number  of  the  yield  per  acre  of  crops.  The  nine 
crops  of  the  United  States  whose  yield  per  acre  through- 
out a  long  period  is  recorded  in  the  Yearbooks  of  the 
Department  of  Agriculture  are:  corn,  wheat,  oats,  bar- 
ley, rye,  buckwheat,  potatoes,  hay,  cotton.'  If,  in  case 
'  The  figures  for  the  yield  per  acre  of  cotton,  1870-1910,  were  oh- 


104         Economic  Cycles:  Their  Law  and  Cause 

of  each  of  these  crops,  the  mean  yield  per  acre  for  the 
years  1890-1899  is  taken  as  a  base,  and  the  yield  per 
acre  for  each  of  the  years  1870-1911  is  expressed  as  a 
ratio  of  the  base,  comparable  indices  for  the  crops  dur- 
ing the  period  of  forty-two  years  will  be  obtained.  In 
order  to  combine  the  nine  series  of  figures  into  a  series 
that  shall  be  representative  of  the  whole  of  agriculture, 
the  several  series  must  be  properly  weighted.  The 
method  of  weighting  that  was  adopted  in  this  particular 
case  was  to  assign  to  each  crop  an  importance  propor- 
tionate to  its  value  as  compared  with  the  total  value  of 
the  nine  crops  in  1911.  The  several  weights  were:  for 
corn,  36;  wheat,  12;  oats,  9;  barley,  3;  rye,  .7;  buck- 
wheat, .3;  potatoes,  6;  hay,  16;  cotton,  17.  The  index 
numbers  are  given  in  Table  I  of  the  Appendix  to  this 
chapter. 

Before  comparing  the  index  number  for  the  yield 
per  acre  of  the  crops  with  the  volume  of  producers' 
goods,  we  must  make  sure  that  we  are  keeping  close 
to  the  results  obtained  from  a  detailed  investigation 
of  our  four  representative  crops.  If  an  index  number  of 
the  four  representative  crops  is  constructed  upon  the 
same  principle  as  the  index  for  the  nine  crops,  how 
closely  would  the  indices  be  correlated?  In  computing 
the  index  of  the  yield  per  acre  of  the  four  representa- 
tive crops,  the  weights  assigned  were:  for  corn,  50; 
hay,  28;  oats,  15;  potatoes,  7.    The  index  is  given  in 

tainrd  from  Circular  32,  Bureau  of  Statistics,  U.  S.  Department  of 
Agriculture.  The  yield  for  1911  was  obtained  from  the  Yearbook 
of  the  Department  of  Agricultur(>,   1911. 


The  Mechanism  of  Cycles  105 

Table  I  of  the  Appendix  to  this  chapter.  The  coeffi- 
cient of  correlation  between  the  index  for  the  four 
representative  crops  and  the  index  for  the  nine  crops, 
is  r  =  .960. 

It  is  a  common  observation  of  writers  on  economic 
crises  that  the  production  of  pig-iron  is  an  unusually 
good  barometer  of  trade.  The  amount  of  pig-iron 
that  is  annually  produced  swells  with  the  activity 
and  volume  of  industry  and  trade,  and  it  is  among  the 
first  commodities  to  indicate  the  general  shrinking  in 
the  ultimate  demand  which  checks  the  activity  of 
trade  and  causes  its  temporary  decline.  Is  there  any 
relation  between  the  movement  of  this  barometer  of 
trade,  the  production  of  pig-iron,  and  the  cycles  of  the 
crops?  Can  it  be  that  the  increase  and  decrease  of  the 
"ultimate  demand"  which  lies  back  of  the  flow  and 
ebb  of  trade  has  its  source  in  the  cyclical  movements 
of  the  yield  per  acre  of  the  crops? 

The  data  for  testing  whether  there  is  a  relation  be- 
tween the  yield  per  acre  of  the  crops  and  the  annual 
production  of  pig-iron  are  the  statistics  of  the  annual 
production  of  pig-iron  and  the  index  numbers  of  the 
yield  per  acre  of  our  nine  crops. 

The  method  of  testing  the  relation  presents  difficul- 
ties, and  as  it  will  be  used  again  to  measure  the  relation 
between  the  cycles  of  crops  and  the  cycles  of  general 
prices,  we  shall  have  a  firmer  grasp  upon  our  problem 
if  we  stop  now  to  gain  a  clear  idea  of  the  terms  that 
continually  occur  in  the  argument.    In  any  one  of  the 


106         Economic  Cycles:  Their  Law  and  Cause 

series  of  figures  that  we  shall  use  there  are  three  distinct 
movements  which  need  to  be  discriminated,  and  when 
any  two  of  the  series  are  compared,  another  important 
characteristic  of  the  series  requires  to  be  taken  into 
account.  The  three  movements  that  are  combined  in 
each  series  are: 

(a)  The  continuous  fall  or  rise  of  the  figures  with  the 
flow  of  time.    This  movement  will  be  referred 
to  as  the  secular  trend  of  the  figures ; 
{h)  The  rhythmical  fluctuation  of  the  figures  about 
their  secular   trend.     \\Tien   this  movement 
superposed  upon  the  secular  trend  is  the  ob- 
ject of  investigation,  the  combined  movement 
will   be   referred   to   as   the   general   cyclical 
movement  of  the  figures.     When  the  rhyth- 
mical movement  unaffected  by  the  complicat- 
ing trend  is  being  considered,  it  will  be  referred 
to  simply  as  the  cycles  of  the  figures; 
(c)  The  year  to  year  temporary  fluctuation  about 
the  general  cycUcal  movement.    These  fluctua- 
tions will  be  referred  to  as  the  deviations  of 
the  figures. 
When  the  cycles  of  any  two  series  are  compared,  it  will 
frequently  happen,  particularly  if  the  one  series  is  the 
cause  of  the  other,  that  there  is  a  considerable  interval 
between  the  corresponding  parts  of  the  cycles  in  the 
two  series.    This  interval  will  be  referred  to  as  the  lag 
of  the  second  series. 

We  shall  be  interested  throughout  the  rest  of  this 
chapter  primarily   in   the  interrelations   of  cycles   of 


The  Mechanism  of  Cycles  107 

crops,  cycles  in  the  activity  of  industry,  and  cycles  in 
general  prices.  But  we  approach  our  general  problem 
by  considering  first  the  temporary  fluctuations  which 
we  have  agreed  to  call  deviations,  and  we  inquire 
whether  there  is  a  relation  between  the  deviations  of 
the  yield  of  the  crops  and  the  deviations  in  the  produc- 
tion of  pig-iron.  The  method  that  was  adopted  was 
first  to  obtain  the  general  cyclical  movements  of  the 
two  series  by  averaging,  in  case  of  each  series,  the 
figures  for  each  year  with  the  figures  that  iimnediately 
preceded  and  followed  the  given  year.  For  example, 
the  index  number  of  the  yield  per  acre  for  the  years 
1870,  1871,  1872,  1873  were  respectively  108,  105,  110, 
99.    The  smoothed  figure  for  the  yield  per  acre  in  1S71 

would  therefore  be — -  =^^^  =  107.7.    Simi- 

3  3 

larly,  the  smoothed  index  for  1872  would  be  104.7.  In 
Tables  II  and  III  of  the  Appendix  to  this  chapter  are 
presented  the  original  and  the  smoothed  figures  for  the 
production  of  pig-iron  and  for  the  index  number  of  the 
yield  per  acre  of  the  nine  crops.  The  statistics  of  the 
production  of  pig-iron  were  obtained  from  the  Statis- 
tical Abstract  of  the  United  States  for  1912,  p.  774. 

After  the  general  cyclical  movements  of  the  two  series 
were  determined,  the  deviations  of  the  actual  figures 
from  the  smoothed  figures  for  each  of  the  years  were 
calculated  for  both  series  of  figures.  These  deviations 
are  also  given  in  Tables  II  and  III  of  the  Appendix  to 
this  chapter.  The  question  upon  which  these  differ- 
ences are  to  throw  Ught  may  be  put  in  this  form:  Is 


108         Economic  Cycles:  Their  Law  and  Cause 

the  deviation  of  the  yield  per  acre  of  the  crops  from  its 
general  cyclical  movement  associated  with  the  devia- 
tion, in  the  following  year,  of  the  production  of  pig- 
iron  from  the  general  cyclical  movement  of  pig-iron? 
The  answer  is  found  by  correlating  the  differences, 
always  remembering  that  the  difference  for  the  yield 
per  acre  in  any  given  year  is  to  be  taken  with  the  dif- 
ference of  the  production  of  pig-iron  in  the  following 
year.    The  coefficient  of  correlation  is  r  =  .254. 

We  come  now  to  the  association  between  the  cycUcal 
movement  of  the  yield  per  acre  of  the  crops  and  the 
cyclical  movement  of  the  production  of  pig-iron.  Each 
of  these  movements  is  superposed  upon  a  rising  secular 
trend,  and  before  we  can  test  the  degree  in  which  the 
cycles  are  related  the  secular  trends  must  be  eliminated. 
If,  as  a  first  approximation,  the  secular  trend  in  each 
case  is  assumed  to  be  linear,  then  by  fitting  a  straight 
line  ^  to  the  data,  it  is  possible  to  calculate  the  fluctua- 
tions of  the  cycles  of  crop  yield  and  of  production  of 
pig-iron  about  their  respective  trends,  and  these  fluctua- 
tions may  be  correlated.  In  Table  IV  of  the  Appendix 
to  this  chapter,  the  data  for  the  calculation  of  the  con- 
nection between  the  cycles  are  given.  In  columns  2 
and  5  are  tabulated  the  general  cyclical  movements  of 

'  The  equations  to  the  hnear  secular  trends  are,  respectively, 
v/  =  .1844a;+98.57,  for  the  yield  per  acre  of  crops;  and  ?/  =  582.71a;+ 
9525,  for  the  production  of  pig-iron.  The  origin  in  the  first  case  is 
at  1871  and  in  the  latter  case,  at  1890.  The  first  equation  was  com- 
l)uted  from  the  data  for  the  years  1871-1906,  and  the  second  equa- 
tion, from  the  data  for  1871  to  1910. 


The  Mechanism  of  Cycles  109 

the  yield  per  acre  of  the  crops  and  of  the  production  of 
pig-iron;  in  columns  3  and  6,  the  values  of  the  linear 
secular  trends  are  given;  and  in  columns  4  and  7,  the 
deviations  of  the  cyclical  movement  from  the  secular 
trend  are  recorded.  These  last  deviations  are  the  ma- 
terial for  calculating  the  connection  between  the  cycles 
of  the  yield  per  acre  of  the  crops  and  the  cycles  of  the 
production  of  pig-iron. 

If  the  deviations  of  the  cycles  from  their  respective 
secular  trends  are  correlated,  the  coefficient  of  correla- 
tion reaches  the  value,  r  =  .625,  but  we  must  not  be 
content  to  assume  that  even  this  relatively  high  co- 
efficient represents  the  full  degree  of  the  relation  be- 
tween the  cyclical  movement  of  the  crops  and  the 
cyclical  movement  of  the  activity  of  industry  as  that 
activity  is  typified  in  the  production  of  pig-iron.  It  is 
quite  likely  that  the  good  or  bad  crops  may  produce 
their  maximum  effect  at  a  considerable  interval  after 
the  period  in  which  the  crops  are  actually  harvested. 
Time  is  required  for  the  changing  productivity  of 
crops  to  work  out  its  maximum  effect,  and  this  causes 
a  lag  in  the  adjustment  of  the  cycles  of  the  activity  of 
industry  to  the  cycles  of  the  yield  of  the  crops.  We 
must  therefore  measure  the  amount  of  the  lag. 

If  instead  of  correlating  the  cycles  of  the  yield  of  the 
crops  and  of  the  production  of  pig-iron  for  correspond- 
ing years,  we  correlate  them  for  lags  of  various  intervals, 
we  shall  find  it  possible  to  determine  the  lag  that  will 
give  the  maximum  coefficient  of  correlation,  and  this 
particular  value  of  the  lag  we  may  then  regard  as  the 


110         Economic  Cycles:  Their  Law  and  Cause 

interval  of  time  required  for  the  cycles  in  the  crops  to 
produce  their  maximum  effect  upon  the  cycles  of  the 
activity  of  industry.  W^ien  the  calculation  of  the  co- 
efficients of  correlation  is  made  according  to  this  plan, 
it  is  found  that  for  a  lag 

Of  zero  years,  r  =  .625; 
Of  one  year,  r  =  .7l9; 
Of  two  j^ears,  r  =  .718; 
Of  three  years,  r  =  .697; 
Of  four  years,    r=.572. 

It  is  clear,  therefore,  that  the  cycles  in  the  yield  per 
acre  of  the  crops  are  intimately  related  to  the  cycles  in 
the  activity  of  industry,  and  that  it  takes  between  one 
and  two  years  for  good  or  bad  crops  to  produce  the 
maximum  effect  upon  the  activity  of  the  pig-iron  in- 
dustry. Figure  23  illustrates  the  general  congruence 
of  the  cycles  of  the  crops  and  of  the  cycles  in  the  produc- 
tion of  pig-iron  when  a  lag  of  two  years  is  eliminated. 

As  to  the  general  question  concerning  the  relation 
between  the  harvests  and  the  activity  of  industry,  we 
may  conclude  from  our  statistical  inquiry  that  there  is 
a  positive,  intimate  connection,  and  very  probably  a 
direct  causal  relation,  between  the  bounty  or  niggardU- 
ness  of  nature  and  the  flow  or  ebb  of  trade.  ^ 

A  NeiD  Type  of  Demand  Curve 

A  moment  ago,  we  saw  that  two  prehminary  problems 

had  to  be  treated  before  we  could  pass  to  the  direct 

^  In  a  later  section  of  the  chapter  the  metliod  that  has  been  used 
in  treating  this  problem  will  be  employed  for  another  purpose  and 
will  then  be  illustrated  in  detail  by  means  of  graphs. 


The  Mechanism  of  ( 'ycles 


111 


Devi  a  f /on  ofthedenfrs/  cyc/icdl  moi'Cment'  of  the  product/ on  ofp/J-zron  /torn  /ts  sec/y/jr  T/cnd. 


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'^tJ*^/  -/e/njjs  <;//  t^/o^  rdojojo  jjjp  J^d pfs// si/ijo^ujuj^/\ouj  /pj'/^/j  /PJ.fL/^^  jlu jo  uoi^p/a^Q 


112         Economic  Cycles:  Their  Law  and  Cause 

consideration  of  the  cause  and  law  of  cycles  of  general 
prices.  The  first  of  these  preliminary  problems,  namely, 
the  influence  of  the  bounty  of  nature  upon  the  volume 
and  acti\dty  of  trade,  we  have  just  discussed,  and  we 
come  now  to  the  second  preliminary  problem,  which 
we  shall  put  in  the  form  of  a  question:  Are  all  demand 
curves  in  a  dynamic  society  of  the  same  type  as  the 
demand  curves  for  the  representative  crops:  corn,  hay, 
oats,  and  potatoes? 

This  question  must  be  answered  as  a  preliminary  to 
the  more  fundamental  inquiry  as  to  the  cause  of  cycles 
of  general  prices,  because  if  we  assume  that  all  demand 
curves  are  of  the  same  negative  type,  we  are  confronted 
with  an  impossibility  at  the  very  beginning  of  our  in- 
vestigation. Upon  the  assumption  that  all  demand 
curves  are  of  the  negative  type,  it  would  be  impossible 
for  general  prices  to  fall  while  the  yield  per  acre  of 
crops  is  decreasing.  In  consequence  of  the  decrease 
in  the  yield  per  acre,  the  price  of  crops  would  ascend, 
the  volume  of  commodities  represented  by  pig-iron 
would  decrease,  and  upon  the  hypothesis  of  the  uni- 
versality of  the  descending  type  of  demand  curves,  the 
prices  of  commodities  like  pig-iron  would  rise.  In  a 
period  of  declining  yield  of  crops,  therefore,  there  would 
be  a  rise  of  prices,  and  in  a  period  of  increasing  yield  of 
crops  there  would  be  a  fall  of  prices.  But  the  facts  are 
exactly  the  contrary.  During  the  long  period  of  falling 
prices  from  1870  to  1890,  there  was  a  decrease  in  the 
yield -per  acre  of  the  crops,  and  during  the  long  period 
of  rising  prices  from  1890  to  1911,  there  was  an  increas- 


The  Mechanism  of  Cycles  113 

ing  yield  of  crops.  It  is  obviously  inadmissible  to 
assume  that  in  a  dynamic  society  there  is  one  law  of 
demand  for  all  commodities.  The  dogma  of  the  uni- 
formity of  the  law  of  demand  is  an  idol  of  the  static 
state. 

If  there  are  differences  in  types  of  demand  curves, 
it  is  quite  likely  that  as  one  type  has  been  illustrated  by 
the  crops,  another  type  will  be  exemplified  by  pure 
producers'  goods.  We  shall  accordingly  investigate 
the  demand  curve  of  pig-iron,  our  representative  pro- 
ducers' good. 

In  Table  V  of  the  Appendix  to  this  chapter  is  con- 
tained the  material  for  the  computation  of  the  law  of 
demand  for  pig-iron.  The  annual  percentage  changes 
in  the  production  of  pig-iron  were  computed  from  the 
figures  of  annual  production,  which  were  taken  from 
the  Statistical  Abstract  for  1912,  p.  774.  It  was  impos- 
sible to  obtain  directly  the  mean  prices  for  which  the 
annual  production  was  sold,  and  consequently  the  per- 
centage change  in  the  mean  price  could  not  be  com- 
puted directly.  The  device  that  was  utilized  to  ap- 
proximate these  percentage  changes  is  illustrated  in 
Table  V  of  the  Appendix.  As  the  data  needed  for  the 
solution  of  the  problem  were  the  annual  percentage 
changes  in  the  mean  price  and  not  the  actual  mean 
annual  prices  themselves,  it  was  regarded  as  sufficient 
for  our  purpose  to  substitute  for  the  unobtainable  an- 
nual percentage  changes  in  the  mean  price,  the  mean 
annual  percentage  changes  in  the  prices  of  representa- 
tive kinds  of  pig-iron.    The  annual  prices  for  the  lead- 


114         Economic  Cycles:  Their  Law  and  Cause 

ing  four  kinds  of  pig-iron  were  obtained  from  the  Statis- 
tical Abstract  for  1912,  p.  572,  and  the  annual  percentage 
changes  in  the  prices  of  the  four  kinds,  together  with 
their  mean  annual  percentage  changes,  are  given  in 
Table  V  of  the  Appendix.  The  second  and  last  columns 
of  Table  V  were  used  in  computing  the  law  of  demand 
for  pig-iron  in  the  United  States. 

The  graph  of  the  law  of  demand  for  pig-iron  is  given 
in  Figure  24.  The  correlation  between  the  percentage 
change  in  the  product  and  the  percentage  change  in  the 
price  is  r  =  .537.  The  equation  to  the  law  of  demand 
is  ?/ =  .521  Ix— 4.58,  the  origin  being  at  {o,o).  Our  re- 
presentative crops  and  representative  producers'  good 
exempUfy  types  of  demand  curves  of  contrary  charac- 
ter. In  the  one  case,  as  the  product  increases  or  de- 
creases the  price  falls  or  rises,  while,  in  the  other  case, 
the  price  rises  with  an  increase  of  the  product  and  falls 
with  its  decrease. 

The  two  preliminary  difficulties  are  now  cleared 
away.  We  know  that  as  the  yield  per  acre  of  the  crops 
increases  the  physical  volume  of  trade  for  producers' 
goods  increases;  and  we  know,  furthermore,  that  the 
law  of  demand  for  a  representative  producers'  good  is 
such  that  as  the  product  increases  the  price  increases. 
If  now  a  third  fact,  which  has  already  been  established, 
be  added  to  these  two,  an  hypothesis  conformable  to 
the  three  facts  may  be  made  which  will  give  a  working 
theory  for  examining  whether  the  cycles  in  crops  pro- 
duce the  cycles  in  general  prices.  The  third  fact  to 
which  reference  is  made  is  that  the  law  of  demand  for 


The  Mechanism  of  Cycles 


115 


uoji-^ic/jo  3yud  ^Lfj.  ui  ^pupLfo  spe^usoj^^j 


116         Econo7nic  Cycles:  Their  Law  and  Cause 

the  crops  falls  during  a  period  of  falling  general  prices, 
and  rises  during  a  period  of  rising  general  prices.  With 
these  facts  in  mind  it  is  not  difficult  to  conceive  how 
general  prices  may  fall  during  a  period  of  diminishing 
yield  per  acre  of  the  crops  and  rise  during  the  period 
that  the  yield  is  increasing.  The  falling  yield  in  the 
crops  would  lead  to  a  diminution  of  the  volume  of  trade, 
a  decline  in  the  demand  for  producers'  goods,  a  fall  in 
the  prices  of  producers'  goods,  a  decrease  in  employ- 
ment, a  fall  of  the  demand  curves  for  crops,  with  the 
final  result  of  a  fall  in  general  prices.  Similarly,  a 
rising  yield  in  the  crops  would  lead  to  an  increase  in 
the  volume  of  trade,  an  increase  in  the  demand  for 
producers'  goods,  an  increase  of  employment,  a  rise 
in  the  demand  curves  for  crops,  with  the  final  result  of 
a  rise  in  general  prices.  Provided  the  interrelation  of 
the  economic  factors  are  in  accordance  with  this  de- 
scription, then  it  would  follow  that  the  cyclical  move- 
ments in  the  yield  of  the  crops  should  be  reproduced 
in  cyclical  movements  of  general  prices.  If  the  actual 
facts  bear  out  this  deduction,  there  can  be  no  doubt 
that  the  cause  and  law  of  economic  cycles  have  been 
discovered. 

The  Fundamental,  Persistent  Cause  of  Economic  Cycles 

To  put  the  theory  to  the  test  of  facts  we  require  an 
index  number  of  general  prices  throughout  the  period 
covered  by  most  of  the  investigation  in  this  Essay — 
the  period  from  1870  to  1911.  There  is  no  one  index 
number  covering  this  period  for  the  United  States,  but 


The  Mechanism  of  Cycles  117 

very  fortunately  there  are  two  series  that  overlap  in  the 
middle  of  the  period,  so  that  it  is  possible  to  construct  a 
series  covering  the  whole  term  of  years.  The  two  series  of 
index  numbers  in  question  are  the  Falkner  index  for  ' '  all 
articles"  extending  from  1870  to  1890,  and  the  index  of 
the  Bureau  of  Labor  for  "all  commodities"  extending 
from  1890  to  1911.  Since  these  two  have  the  year  1890 
in  common  it  is  possible,  by  applying  the  simple  rule  of 
proportion,  to  reduce  the  Falkner  series  to  the  base  of 
the  series  published  by  the  Bureau  of  Labor.  The  two 
original  series  and  the  continuous  series  are  given  in 
Table  VI  of  the  Appendix  to  this  chapter. 

The  test  of  the  theory  that  the  cause  and  law  of 
economic  cycles  are  the  cyclical  movements  of  the 
yield  per  acre  of  the  crops  will  be  given  in  answer  to  two 
questions:  First,  are  the  deviations  of  the  indices  of 
general  prices  from  their  general  cyclical  movement 
correlated  with  the  deviations  of  the  indices  of  the  yield 
per  acre  of  the  crops  from  their  general  cyclical  move- 
ment? Secondly,  are  the  cycles  of  prices  and  the  cycles 
of  crops  correlated?  The  answers  to  these  two  questions 
are  the  substance  of  the  following  paragraphs. 

In  Tables  III  and  VI  of  the  Appendix  to  this  chapter 
are  given  the  indices  of  the  yield  per  acre  of  the  crops 
and  the  indices  of  general  prices.  The  Tables  like- 
wise contain  the  smoothed  indices  and  the  deviations  of 
the  actual  indices  from  the  smoothed  indices.  The 
smoothed  series  were  obtained  in  the  manner  that  was 
described  when  the  relation  between  the  yield  of  the 
crops  and  the  production  of  pig-iron  was  being  treated. 


118         Ecojiomic  Cycles:  Their  Law  and  Cause 

It  will  be  recalled  from  that  description  that  the 
smoothed  index  for  any  given  year  is  the  mean  of  three 
actual  indices:  the  actual  index  for  the  given  year,  the 
actual  index  for  the  year  preceding  the  given  year,  and 
the  actual  index  for  the  year  following  the  given  year. 
The  quantities  whose  correlation  is  in  question  are  the 
deviations  of  the  actual  indices  of  general  prices,  and  of 
yield  per  acre,  from  their  respective  smoothed  series. 
The  results  of  the  computation  are  as  follows : 

From  1870-1911,  r=.303, 
From  1870-1890,  r  =  .370, 
From  1890-1911,  r  =  .250. 

In  the  first  row  the  correlations  were  obtained  from 
the  continuous  series  in  which  the  Falkner  index  was 
adjusted  to  the  index  of  the  Bureau  of  Labor.  In  the 
second  row  the  correlations  were  derived  from  the 
Falkner  index  unaltered.  In  the  third  row  the  correla- 
tions were  computed  from  the  index  of  the  Bureau  of 
Labor.  We  infer  that  the  deviations  from  their  general 
cyclical  movement  of  thejndices  of  general  prices  vary 
directly  with  the  deviation  from  their  general  cyclical 
movement  of  the  indices  of  the  yield  per  acre  of  the 
crops. 

The  second  of  the  two  questions  as  to  the  cause  and 
law  of  the  cycles  of  general  prices  was  stated  in  this 
form:  Are  the  cycles  of  prices  and  the  cycles  of  crops 
correlated?  The  preceding  paragraphs  have  presented 
the  results  of  the  in(|uiry  as  to  the  relation  between  the 
deviations  of  actual  prices  and  of  yield   from   their 


The  Mechanism  of  Cycles  119 

respective  general  cyclical  movements.  The  present 
question  concerns  the  relation  of  the  cyclical  move- 
ments themselves,  after  their  respective  secular  trends 
have  been  eliminated. 

It  will  be  recalled  that  the  general  cyclical  movements 
were  obtained  by  a  process  of  smoothing  the  actual 
series  of  the  indices  of  prices  and  of  yield  per  acre,  the 
process  consisting  in  the  formation  of  a  progressive 
mean  of  the  indices  for  three  consecutive  years.  These 
smoothed  series,  which  are  given  in  Tables  III  and  VI 
of  the  Appendix  to  this  chapter,  form  the  data  of  the 
present  investigation. 

The  method  of  the  investigation  is  presented  in  Fig- 
ures 25,  26,  27.  In  the  first  of  these  three  Figures,  the 
general  cyclical  movements  of  prices  and  of  yield  per 
acre  are  described  according  to  the  data  of  Tables  III 
and  VI.  The  graphs  bring  out  clearly  the  rhythmical 
motions  of  both  prices  and  yield  and  a  comparison 
of  the  curves  suggests  that  the  price  curve  is  a  lagging 
reproduction  of  the  yield  curve.  But  before  the  amount 
of  the  lag  and  the  degree  of  correlation  between  the 
cycles  can  be  computed,  the  secular  trends  in  the  two 
series  of  values  must  be  eliminated.  From  Figure  25  it 
is  apparent  that  the  price  cycles  move  upon  a  falling 
secular  trend  while  the  yield  cycles  move  upon  a  rising 
secular  trend.  If  it  is  assumed  as  a  first  approximation 
that  these  secular  trends  are  both  linear,  the  equation  to 
the  trend  for  prices  is  ?/  =  —  .3702x  + 122.01,  and  to  the 
trend  for  the  yield  per  acre,  y  =  .1844x+98.57,  the  ori- 
gin, in  the  former  case,  being  at  1875  and,  in  the  latter, 


120         Economic  Cycles:  Their  Law  and  Cause 


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The  Mechanism  of  Cycles 


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122         Economic  Cycles:  Their  Law  and  Cause 

at  1871.^  These  two  equations  make  it  possible  to 
eliminate  the  secular  trends  upon  which  move  the 
cycles  of  prices  and  the  cycles  of  yield.  The  results  of 
the  calculations  are  given  in  Table  VII  of  the  Appendix 
to  this  chapter. 

Figure  26  presents  the  cycles  of  yield  per  acre  and  the 
cycles  of  general  prices  after  the  secular  trends  upon 
which  they  were  respectively  superposed  have  been 
eliminated.  It  is  quite  evident,  now,  from  the  appear- 
ance of  the  graphs,  that  the  cycles  of  yield  per  acre  and 
the  C3''cles  of  general  prices  are  closely  related,  and  that 
the  cycles  of  prices  lag  several  years  behind  the  cycles  of 
crops.  What  is  the  amount  of  the  lag  and  how  closely 
are  the  cycles;  correlated?  Both  of  these  questions  may 
be  answered  at  once  by  following  the  method  that  was 
adopted  to  measure  the  lag  in  the  cycles  of  pig-iron 
production.  If  the  cycles  of  the  yield  per  acre  are 
correlated  ^  with  the  cycles  of  general  prices  we  find,  for 
a  lag  of  three  years  in  general  prices,  r  =  .786;  for  a  lag 
of  four  years,  r  =  .800;  for  a  lag  of  five  years,  r  =  .710. 
The  cycles  in  the  yield  per  acre  of  the  crops  are,  there- 
fore, intimately  connected  with  the  cycles  of  general 
prices,  and  the  lag  in  the  cycles  of  general  prices  is 
approximately  four  years. 

Figure  27  presents  the  two  series  of  cycles  with  the 
lag  of  four  years  in  the  cycles  of  prices  eliminated.    It  is 

1  The  first  equation  was  computed  from  the  data  for  1875-1910, 
and  the  second  equation,  from  the  data  for  1871-1906. 

^  The  data  for  the  calculation  are  given  in  columns  4  and  7  of 
Table  VII  in  the  Appendix  to  this  chapter. 


The  Mechanism  of  Cycles 


123 


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124         Economic  Cycles:  Their  Law  and  Cause 

surely  not  an  exaggeration  to  say  that  the  congruence  of 
the  two  rhythmical  movements  of  crop  yield  and  general 
prices  is  so  close  as  to  justify  the  inference  that  the  one 
series  is  the  cause  of  the  other.  Every  important 
rhythmical  feature  of  the  yield  curve  is  reproduced  in 
the  price  curve :  the  long  cycle  which  in  both  curves  dips 
below  the  horizontal  between  1880  and  1900,  and  the 
smaller  superposed  cycles  that  move  upon  the  large 
ground-swell.  The  one  apparent  exception  occurs  in 
the  price  movement  between  1887  and  1891  in  which 
the  price  curve  does  not  keep  close  to  the  yield  curve. 
But  this  is  not  a  real  exception.  For,  in  the  first  place, 
the  price  curve  is  convex  between  these  limits,  that 
is  to  say,  it  shows  a  tendency  to  conform  to  the  yield 
curve;  and,  in  the  second  place,  since  in  the  price 
curve  a  lag  of  four  years  has  been  eliminated,  the  date 
at  which  the  disturbance  occurs  is  really  four  years 
later  than  would  appear  from  the  dates  on  the  chart. 
That  would  place  the  disturbance  at  about  1893,  which 
was  the  year  of  the  panic  with  extraordinary  condi- 
tions in  the  state  of  the  currency  and  the  money  mar- 
ket. 

Considering  the  high  correlation  between  the  two 
series  of  cycles  and  the  harmony  of  their  congruence 
with  the  theory  of  economic  cycles  embodied  in  this 
Essay,  we  conclude  that  the  cycles  of  the  yield  per 
acre  of  the  crops  cause  the  cycles  of  general  prices  and 
that  the  law  of  the  cycles  of  crops  is  the  law  of  the  cycles 
of  general  prices. 


The  Mechanism  of  Cycles  125 

The  chief  results  of  this  chapter  may  be  summarized 
in  a  few  propositions : 

(1)  The  yield  per  acre,  for  the  whole  of  the  United 

States,  of  the  four  representative  crops,  corn, 
hay,  oats,  and  potatoes  is  so  closely  correlated 
with  the  yield  per  acre  of  these  crops  in  Illinois 
as  to  render  it  very  probable  that  the  cause  of 
the  cycles  of  the  yield  in  the  United  States 
is  the  same  as  the  cause  of  the  cycles  in  Illinois. 
The  meteorological  cause  of  the  rhythmical 
changes  in  the  yield  of  Illinois  has  been  dis- 
cussed in  an  earlier  chapter. 

(2)  The  prices   in   the   United   States   of   the  four 

representative  crops  are  as  closely  related  to 
the  yield  per  acre  of  the  crops  as  the  prices  are 
related  to  the  total  supply  of  the  respective 
crops.  For  the  purpose  of  prediction  of  prices, 
therefore,  the  yield-price  curve  is  as  useful  as 
the  demand  curve. 

(3)  The  curves  representing  the  relation  between  the 

yield  per  acre  and  price,  in  case  of  the  four 
representative  crops,  fall  during  a  period  of 
falling  yield  and  falUng  general  prices,  and 
rise  under  the  contrary  circumstances. 

(4)  The  falling  or  rising  yield  per  acre  of  the  crops 

leads  to  a  falling  or  rising  volume  of  trade  in 
producers'  goods.  If  the  production  of  pig- 
iron  be  taken  as  a  representative  producers' 
good,  then 

(a)  The  deviations  of  the  annual  production 


126         Economic  Cycles:  Their  Law  and  Cause 

of  pig-iron  from  the  general  cyclical 
movement  in  the  production  of  pig-iron 
are  directly  correlated  with  the  devia- 
tions, in  the  preceding  year,  of  the 
yield  per  acre  of  the  crops  from  their 
general  cyclical  movement ; 
(b)  When  the  lag  in  the  production  of  pig- 
iron  and  the  secular  trend  in  both  the 
production  of  pig-iron  and  in  the  yield 
per  acre  of  the  crops  are  eliminated,  the 
cycles  of  production  of  pig-iron  are  very 
closely  correlated  with  the  cycles  of  the 
yield  per  acre  of  the  crops.  The  coeffi- 
cient of  correlation  is  r  =  .719. 

(5)  Unlike  the  law  of  demand  for  the  crops,  the  law  of 

demand  for  a  representative  producers'  good 
is  such  that  as  the  supply  increases  the  price 
rises,  and  as  the  supply  decreases  the  price 
falls. 

(6)  With  the  falling  of  the  yield  per  acre  of  the  crops 

there  is  a  falling  volume  of  trade,  a  falling 
price  of  producers'  goods,  an  increase  in  un- 
employment, and  a  fall  in  the  yield-price 
curves  for  the  crops.  The  contrary  conditions 
prevail  under  a  rising  yield  per  acre  of  the 
crops. 

(7)  The  ultimate  effect  upon  general  prices  of  the 

process  described  in  (6)  is  that 

(a)  The  deviations  of  general  prices  from 
their   general   cyclical   movement   are 


The  Mechanism  of  Cycles  127 

directly  correlated  with  the  deviations 
of  the  yield  per  acre  of  the  crops  from 
their  general  cycUcal  movement ; 
(b)  When  the  lag  in  general  prices  and  the 
secular  trend  in  both  prices  and  yield 
per  acre  are  eliminated,  the  cycles  of 
general  prices  are  very  closely  corre- 
lated with  the  cycles  of  the  yield  per 
acre  of  the  crops.  The  coefficient  of 
correlation  is  r  =  .800. 

(8)  The  law  of  the  cycles  of  crops  is  the  law  of  the 

cycles  in  the  activity  of  industry  and  the 
law  of  the  cycles  of  general  prices. 

(9)  The  fundamental,  persistent  cause  of  the  cycles 

in  the  activity  of  industry  and  of  the  cycles  of 
general  prices  is  the  cyclical  movement  in  the 
yield  per  acre  of  the  crops. 


128         Economic  Cycles:  Their  Law  and  Cause 


APPENDIX 


TABLE  I. — Index  Number  of  the  Yield  Per  Acre  of  Crops 


Year 

Index  for 

Nine  Crops 

Index  for 
Four  Crops 

Year 

Index  for 
Nine  Crops 

Index  for 
Four  Crops 

1870 

108 

109 

1891 

108 

107 

1871 

105 

113 

1892 

98 

93 

1872 

110 

115 

1893 

92 

95 

1873 

99 

98 

1894 

90 

85 

1874 

88 

88 

1895 

102 

104 

1875 

110 

114 

1896 

102 

111 

1876 

98 

101 

1897 

102 

102 

1877 

106 

110 

1898 

111 

108 

1878 

109 

113 

1899 

105 

108 

1879 

111 

114 

1900 

104 

105 

1880 

106 

107 

1901 

89 

83 

1881 

82 

82 

1902 

114 

117 

1882 

100 

99 

1903 

107 

111 

1883 

97 

100 

1904 

114 

117 

1884 

101 

105 

1905 

116 

121 

1885 

98 

102 

1906 

119 

120 

1886 

93 

93 

1907 

106 

107 

1887 

89 

85 

1908 

109 

110 

1888 

100 

103 

1909 

108 

111 

1889 

104 

106 

1910 

109 

113 

1890 

89 

86 

1911 

99 

95 

The  Mechanism  of  Cycles 


129 


TABLE  II. — The  General  Cyclical  Movement  and  the  Dif- 
ferences OF  THE  Production  of  Pig-Iron  in  the  United 
States 


Year 

Produc- 
tion OP 
Pig-iron 
IN  Thou- 
sands OF 
Long 
Tons 

The  Gen- 
eral Cy- 
clical 
Move- 
ment 
(Progres- 
sive Av- 
erages of 
Three 
Years) 

Differ- 
ence Be- 
tween 
THE  Ac- 
tual 
Produc- 
tion  AND 
THE  Gen- 
eral Cy- 
clical 
Move- 
ment 

Year 

Produc- 
tion of 
Pig-iron 
IN  Thou- 
sands of 
Long 
Tons 

The  Gen- 
eral Cy- 
clical 
Move- 
ment 
(Progres- 
sive Av- 
erages OF 
Three 
Years) 

Differ- 
ence Be- 
tween the 
Actual 
Produc- 
tion AND 
THE  Gen- 
eral Cy- 
clical 
Move- 
ment 

1870 

1,665 

1891 

8,280 

8,880 

—  600 

1871 

1,707 

1,974 

1892 

9,157 

8,187 

+  970 

1872 

2,549 

2,272 

-f277 

1893 

7,125 

7,647 

—  522 

1873 

2,561 

2,504 

+  57 

1894 

6,658 

7,743 

— 10S5 

1874 

2,401 

2,329 

-f  72 

1895 

9,446 

8,242 

+  12j4 

1875 

2,024 

2,(J9S 

—  74 

1896 

8,623 

9,241 

—  018 

1876 

1,869 

1,987 

—118 

1S97 

9,653 

10,017 

—  364 

1877 

2,067 

2,079 

—  12 

189S 

11,774 

11,683 

+     91 

1878 

2,301 

2,370 

—  69 

1899 

13,621 

13,061 

+  5G0 

1879 

2,742 

2,626 

+  116 

1900 

13,789 

14,429 

—  640 

1880 

3,835 

3,574 

-f261 

1901 

15,878 

15,829 

+     49 

1881 

4,144 

4,201 

—  57 

1902 

17,821 

17,230 

+  585 

1882 

4,623 

4,454 

+  169 

1903 

18,009 

17,442 

+  567 

1883 

4,596 

4,439 

+  157 

1904 

16,497 

19,166 

—2669 

1884 

4,098 

4,246 

—148 

1905 

22,992 

21,599 

+  1393 

1885 

4,045 

4,609 

—564 

1906 

25,307 

2t,693 

+  614 

1886 

5,683 

5,382 

+301 

1907 

25,781 

22,341 

+3440 

1887 

6,417 

6,197 

+220 

1908 

15,936 

22,501 

—6568 

1888 

6,490 

6,837 

—347 

1909 

25,795 

23,012 

+2783 

1889 

7,604 

7,766 

—162 

1910 

27,301 

23,583 

+  1721 

1890 

9,203 

8,362 

+841 

1911 

23,650 

130         Economic  Cycles:  Their  Law  and  Cause 


TABLE  III. — The  General  Cyxlical  Movement  and  the  Dif- 
ferences OF  THE  Index  Number  of  the  Yield  Per  Acre  of 
Nl\e  Crops 


The  Gen" 

Differ- 

The Gen- 

Differ- 

ERAL Cy- 

ence Be- 

eral Cy- 

ence  Be- 

Index of 

clical 

tween  the 

Index  of 

CIICAL 

tween  THE 

Yield 

ISIOVE- 

Actual 

Yield 

Move- 

Actual 

Year 

Per 

MENT 

Index  and 

Year 

Per 

ment 

Index  and 

Acre 

(Progres- 

the Gen- 

Acre 

fPROGRES- 

THE  Gen- 

(Nine 

sive  Av- 

eral Cy- 

(Nine 

sive  Av- 

eral Cy- 

Crops) 

erages  OF 

clical 

Crops) 

erages   OF 

clical 

Three 

Move- 

Three 

Move- 

Years) 

ment 

Years) 

ment 

1870 

108 

1891 

108 

98.3 

+  9.7 

1871 

105 

107.7 

—  2.7 

1892 

98 

99.3 

—  1.3 

1872 

110 

104.7 

+  5.3 

1893 

92 

93.3 

—  1.3 

1873 

99 

99.0 

0.0 

1894 

90 

94.7 

—  4.7 

1874 

88 

99.0 

—11.0 

1895 

102 

98.0 

+  4.0 

1875 

110 

98.7 

+  11.3 

1896 

102 

102.0 

0.0 

1876 

98 

104.7 

—  6.7 

1897 

102 

105.0 

—  3.0 

1877 

100 

104.3 

+   1.7 

1898 

111 

106.0 

+  5.0 

1878 

109 

108.7 

+      .3 

1899 

105 

106.7 

—  1.7 

1879 

111 

108.7 

+  2.3 

1900 

104 

99.3 

+  4.7 

1880 

106 

99.7 

+  6.3 

1901 

89 

102.3 

—13.3 

1881 

82 

96.0 

—14 . 0 

1902 

114 

103.3 

+  10.7 

1882 

100 

93.0 

+  7.0 

1903 

107 

111.7 

—  4.7 

1883 

97 

99.3 

—  2.3 

1904 

114 

112.3 

+   1.7 

1884 

101 

98.7 

+  2.3 

1905 

116 

116.3 

—     .3 

1885 

98 

97.3 

+      .7 

1906 

119 

113.7 

+  5.3 

1886 

93 

93.3 

—      .3 

1907 

106 

111.3 

—  5.3 

1887 

89 

94.0 

—  5.0 

1908 

109 

107.7 

+  1.3 

1888 

100 

97.7 

+  2.3 

1909 

108 

108.7 

—     .7 

1889 

104 

97.7 

+  6.3 

1910 

109 

105.3 

+  3.7 

1890 

89 

100.3 

—11.3 

1911 

99 

The  Mechanis7n  of  Cycles 


131 


TABLE  IV. — Cycles  of  Yield  Per  Acre  of  Crops  and  Cycles 
OF  Production  of  Pig-iron 


Year 

General 
Cyclical 
Move- 
ment 
OF  Yield 
Per  Acre 
OF  Crops 

Ordin.^te 

OF   THE 

Secular 
Trend 

Cycles 
OF  Yield 
Per  Acre 
OF  Crops 

General 
Cyclical 
move.ment 
OF  Produc- 
tion OF  Pig- 
iron,  in 
Thousands 
OF  Tons 

Ordinate 
OF  the 

Secular 
Trend 

Cycles  of 
Production 
OF  Pig-iron 

1871 

107.7 

98. 6 

+ 

9.1 

1,974 

—    1,546 

+3,520 

1S72 

104.7 

9S .  8 

+ 

5.9 

2,272 

—      964 

+3,236 

1873 

99.0 

9S.9 

+ 

.1 

2,504 

—      381 

+2,885 

1874 

99.0 

99.1 

— 

.1 

2,329 

202 

+2,127 

1875 

98.7 

99.3 

— ■ 

.4 

2,098 

784 

+  1,314 

1876 

104.7 

99.5 

+ 

5.2 

1,987 

1,367 

+    620 

1877 

104.3 

99.7 

+ 

4.6 

2,079 

1,950 

+    129 

1878 

108.7 

99.9 

+ 

8.8 

2,370 

2,532 

—    162 

1879 

108.7 

100.0 

+  8.7   1 

2,626 

3,115 

—    489 

1880 

99.7 

100.2 

— 

.5 

3,574 

3,698 

—    124 

1881 

96.0 

100.4 

— 

4.4 

4,201 

4,281 

—      80 

1882 

93  0 

100.6 

— 

7.6 

4,454 

4,863 

—    409 

1883 

99.3 

100.9 

— 

1.6 

4,439 

5,446 

—1,007 

1884 

98.7 

101.0 

— 

2.3 

4,246 

6,029 

—1,783 

1885 

97.3 

101.2 

— 

3.9 

4,609 

6,611 

—2,002 

1886 

93.3 

101.3 

— 

8.0 

5,382 

7,194 

—1,812 

1887 

94.0 

101.5 

— ■ 

7.5 

6,197 

7,777 

—1,580 

1888 

97.7 

101.7 

— 

4.0 

6,837 

8,360 

—1,523 

1889 

97.7 

101.9 

— 

4.2 

7,766 

8,942 

—1,176 

1890 

100.3 

102 . 1 

— 

1.8 

8,362 

9,525 

—1,163 

1891 

98.3 

102.3 

— 

4.0 

8,880 

10,108 

—1,228 

1892 

99.3 

102.4 

— ■ 

3.1 

8,187 

10,690 

—2,503 

1893 

93.3 

102.6 

— 

9.3 

7,647 

11,273 

—3,626 

1894 

94.7 

102.8 

— 

8.1 

7,743 

11,856 

—4,112 

1895 

98.0 

103.0 

— 

5.0 

8,242 

12,439 

—4,197 

1896 

102.0 

103.2 

— 

1.2 

9,241 

13,021 

—3,780 

1897 

105 . 0 

103.4 

+ 

1.6 

10,017 

13,604 

—3,587 

1898 

lOG.O 

103.5 

+ 

2.5 

11,683 

14,187 

—2,504 

1899 

106.7 

103.7 

+ 

3.0 

13,061 

14,769 

—  1,708 

1900 

99.3 

103.9 

— 

4.6 

14,429 

15,352 

—    923 

1901 

102.3 

104.1 

— 

1.8    i 

15,829 

15,935 

—    106 

1902 

103.3 

104.3 

— 

1.0  ! 

17,236 

16,518 

+    718 

1903 

111.7 

104.5 

+ 

7.2 

17,442 

17,100 

+    342 

1904 

112.3 

104.7 

+ 

7.6 

19,166 

17,6S3 

+  1,483 

1905 

116.3 

104.8 

+  11.5 

21,599 

1S,2(;6 

+3,333 

1906 

113.7 

105.0 

+ 

8.7 

24,693 

1S,84S 

+5,845 

1907 

111.3 

105.2 

+ 

6.1 

22,341 

19,4:51 

+2,910 

1908 

107.7 

105.4 

+ 

2.3 

22,504 

20,014 

+  2,490 

1909 

108.7 

105 . 5 

+ 

3.2 

23,012 

20,596 

+2,416 

1910 

105.3 

105.7 

— ■ 

.4 

25,583 

21,179 

+4.404 

132         Economic  Cycles:  Their  Law  and  Cause 


TABLE  y. — Percentage  Change  in  the  Production  of  Pig- 
iron  AND  Mean  Percentage  Change  in  the  Price  of  Pig-iron 


1 

YE.^.R 

Percent- 

TAGE 

Change  in 
THE  Pro- 
duction OK 
Pig-iron 

Percentage  Change  in  the  Price  op  Piq-iron 

Mean 
Perce.nt- 

age 

Change  in 

Price  of 

Pig-iron 

No.  1 
Foundry 
AT  Phila- 
delphia 

Gray 
Forge  at 
Philadel- 
phia 

Gray 
Forge 
Lake  Ore 
AT  Pitts- 
burg 

Bessemer 

AT 

Pittsburg 

1870 

1871 

+  2.52 

+  5.57 

+  5.57 

1872 

-f49.33 

+39.51 

+39.51 

1873 

+     .47 

—12.57 

—12.57 

1874 

—  6.25 

—29.45 

—24.13 

—26.79 

1875 

—15.70 

—15.44 

—12.85 

—14.14 

1876 

—  7.66 

—13.08 

—  8.15 

—10.61 

1877 

+  10.59 

—14.74 

—  5.24 

—  9.99 

1878 

+  11.32 

—  6.61 

—12.18 

—  9.39 

1879 

+  19.17 

+22.92 

+22.44 

+22.68 

1880 

+39.86 

+31.12 

+26.32 

+28.72 

1881 

+  8.06 

—11.62 

—18.01 

—14.82 

1882 

+  11.56 

+  2.38 

+  3.92 

+  3.15 

1883 

—     .58 

—13.00 

—14.47 

—20.13 

—15.87 

1884 

—10.84 

—11.64 

—  8.38 

—  9.82 

—  9.95 

1885 

—  1.29 

—  9.14 

—12.03 

—11.07 

—10.75 

1886 

+41.61 

+  4.00 

+  5.26 

+  8.58 

+  5.95 

1887 

+  12.92 

+  11.87 

+  8.48 

+  14.72 

+  12.71 

+  11.95 

1888 

+  1.14 

—  9.79 

—  8.88 

—15.93 

—18.67 

—13.32 

1889 

+  17.16 

—  5.93 

—  4.50 

—  4.00 

+  3.57 

—  2.72 

1890 

+21.03 

+  3.66 

+  2.20 

+  2.80 

+  4.83 

+  3.37 

1891 

—10.03 

—  4.83 

—  8.22 

—10.90 

—15.47 

—  9.85 

1892 

+  10.59 

—10.10 

—  6.75 

—  8.89 

—  9.91 

—  8.91 

1893 

—22.19 

—  7.81 

—  5.98 

—  8.12 

—10.44 

—  8.09 

1894 

—  6.55 

—12.81 

—15.71 

—17.16 

—11.58 

—14.32 

1895 

+41.87 

+  3.48 

+  7.08 

+  12.21 

+  11.78 

+  8.64 

1896 

—  8.71 

—  1.15 

—  3.48 

—  5.03 

—  4.56 

—  3.55 

1897 

+  11.91 

—  6.56 

—  5.50 

—13.09 

—16.56 

—10.43 

1898 

+21.97 

—  3.64 

—  2.39 

+  1.66 

+  1.97 

—     .60 

1899 

+  15.70 

+66.04 

+62.27 

+82.14 

+84.22 

+73.67 

1900 

+  1.23 

+  3.20 

—     .66 

+  1.08 

+  2.42 

+  1.51 

1901 

+  15.15 

—20.57 

—14.61 

—15.98 

—18,27 

—17.36 

1903 

+  12.24 

+39.82 

+36.36 

+37.25 

+29.76 

+35.80 

1903 

+  1.05 

—10.23 

—10.78 

—10.11 

—  8.18 

—10.07 

1904 

—  8.40 

—21.84 

—20.20 

—26.43 

—27.50 

—23.99 

1905 

+39.37 

+  14.84 

+  13.97 

+21.18 

+  18.90 

+  17.22 

1906 

+  10.07 

+  17.34 

+  14.18 

+  16.45 

+  19.44 

+  16.85 

1907 

+  1.87 

+  13.87 

+  18.38 

+  18.31 

+  16.89 

+  16.86 

1908 

—38.19 

—25  91 

—25.36 

—29.23 

—25.26 

-26.44' 

1909 

+61.87 

+      .62 

+  2.61 

+  2.10 

+  1.99 

+  1.83 

1910 

+  5.85 

—  2.53 

—  2.54 

—  1.99 

—  1.26 

—  2.08 

1911 

—13.38 

—  9.50 

—  8.21 

—  8.33 

—  8.61 

—  8.66 

1912 

+25 .  70 

+  5.41 

+  6.65 

+  4.08 

+  1.46 

+  4.40 

The  Mechanism  cf  Cycles 


133 


TABLE  VI. — The    Index   Number   of   General   Prices. 
General  Cyclical  Movement  and  its  Differences 


Its 


Falkner's 

j 

'  lENERA  L 

Difference 

Year 

Falkner's 
Index   of 
Prices  of 
"All  Ar- 
ticles" 

Bureau  of 
Labor's 
Inde.x  of 
Prices  of 
"  All  Com- 
modities" 

Index 

Adjusted 

TO  THE 

Base  of 
THE  Bur- 
eau  OF 
Labor 

The  Co.v- 

TINUOUS 

I.vdex   of 
Prices 

CrCLICAL 
MOVEME.NI 

OF  THE 
CONTI.NU- 

ous  Index 
OF  Prices 

Between 
THE  .A.ctual| 
Index  and 
THE  Gen- 
eral Cy- 
clical 
Movement 

1870 

117.3 

143.5 

143.5 

1871 

122.9 

150.3 

150.3 

149.  S 

+    .') 

1872 

127.2 

155.6 

155 . 6 

151.7 

+3.9 

1873 

122.0 

149.2 

149.2 

150.3 

—1.1 

1874 

119.4 

146.0 

146.0 

144.6 

+  1.4 

1875 

113.4 

138.7 

138.7 

137.6 

+  1.1 

1876 

104.8 

128.2 

1-28.2 

131.5 

—3.3 

1877 

104.4 

127.7 

127.7 

126.0 

+  1.7 

1878 

99.9 

122.2 

122.2 

122.7 

—   .5 

1879 

96.6 

118.2 

118.2 

123.7 

—5 . 5 

1880 

106.9 

130.8 

130.8 

126.1 

+4.7 

1881 

105.7 

129.3 

129.3 

130.9 

—1.6 

1882 

108.5 

132.7 

132.7 

130.6 

+2.1 

1883 

106.0 

129. 7i 

129.7 

12S.0 

+  1.7 

1884 

99.4 

121.6 

121.6 

121.7 

—   .1 

1885 

93.0 

113.8 

113.8 

115.9 

—2.1 

1886 

91.9 

112.4 

112.4 

113.2 

—   .8 

1887 

92.6 

113.3 

113.3 

113.6 

—   .3 

1888 

94.2 

115.2 

115.2 

114.6 

+    .6 

1889 

94.2 

115.2 

115.2 

114.4 

+    .8 

1890 

92.3 

112.9 

112.9 

113.3 

—   .4 

1891 

111.7 

111.7 

110.2 

+  1.5 

1892 

106.1 

106.1 

107.8 

—1.7 

1893 

105.6 

105.6 

102.6 

+3.0 

1894 

96.1 

96.1 

98.4 

—2.3 

1895 

93.6 

93.6 

93.4 

+    .2 

1896 

90.4 

90.4 

91.2 

—   .8 

1897 

89.7 

89.7 

91.2 

—1.5 

1898 

93.4 

93.4 

94.9    ! 

—1.5 

1899 

101.7 

101.7 

101.9     1 

—   .2 

1900 

110.5 

110.5 

103.9 

+3.6 

1901 

108.5 

108.5 

110.0 

—2.1 

1902 

112.9 

112.9 

111.7 

+  1.2 

1903 

113.6 

113.6 

113.2 

+    .4 

1904 

113.0 

113.0 

114.2     1 

—1.2 

1905 

115.9 

115.9 

117.1     i 

—1.2 

1906 

122.5 

122.5 

122.6 

—   .1 

1907 

129.5 

129.5 

124.9 

+4  6 

1908 

122.8 

122.8 

126.3 

—3.5 

1909 

126.5 

126.5 

127.0 

—  .5 

1910 

131.6 

131.6 

129.1 

+2.5 

1911 

129.3 

129.3 

134         Economic  Cycles:  Their  Law  and  Cause 


TABLE  VII. — Cycles  of  Yield  Per  Acre  op  Crops  and  Cycles 
OF  General  Prices 


Year 

General 
Cyclical 

Move- 
ment OF 
Yield  Per 
Acre  of 

Crops 

Ordinates 

OF  the 

Secular 

Trend 

Cycles  of 
the  Yield 
Per  Acre 
of  Crops 

General 
Cyclical 

Move- 
ment OF 
General 

Prices 

Ordinates 
OF  the 
Secular 
Trend 

Cycles  of 

General 

Prices 

1871 

107.7 

98.6 

+  9.1 

149.8 

123.5 

+26.3 

1872 

104.7 

98.8 

+  5.9 

151.7 

123.1 

+28.6 

1873 

99.0 

98.9 

+      .1 

150.3 

122.8 

+27.5 

1874 

99.0 

99.1 

—     .1 

144.6 

122.4 

+22.2 

1875 

98.7 

99.3 

—     .4 

137.6 

122.0 

+  15.6 

1876 

104.7 

99.5 

-f  5.2 

131.5 

121.6 

+  9.9 

1877 

104.3 

99.7 

+  4.6 

126.0 

121.3 

+  4.7 

1878 

108.7 

99.9 

+  8.8 

122.7 

120.9 

+  1.8 

1879 

108.7 

100.0 

+  8.7 

123.7 

120.5 

+  3.2 

1880 

99.7 

100.2 

—     .5 

126.1 

120.2 

+  5.9 

1881 

96.0 

100.4 

—  4.4 

130.9 

119.8 

+  11.1 

1882 

93.0 

100.6 

—  7.6 

130.6 

119.4 

+  11.2 

1883 

99.3 

100.9 

—  1.6 

128.0 

119.0 

+  9.0 

1884 

98.7 

101.0 

—  2.3 

121.7 

118.7 

+  3.0 

1885 

97.3 

101.2 

—  3.9 

115.9 

118.3 

—  2.4 

1886 

93.3 

101.3 

—  8.0 

113.2 

117.9 

—  4.7 

1887 

94.0 

101.5 

—  7.5 

113.6 

117.6 

—  4.0 

1888 

97.7 

101.7 

—  4.0 

114.6 

117.2 

—  2.6 

1889 

97.7 

101.9 

—  4.2 

114.4 

116.8 

—  2.4 

1890 

100.3 

102.1 

—  1.8 

113.3 

116.5 

—  3.2 

1891 

98.3 

102.3 

—  4.0 

110.2 

116.1 

—  5.9 

1892 

99.3 

102.4 

—  3.1 

107.  S 

115.7 

—  7.9 

1893 

93.3 

102.6 

—  9.3 

102.6 

115.3 

—12.7 

1894 

94.7 

102.8 

—  8.1 

98.4 

115.0 

—16.6 

1895 

98.0 

103.0 

—  5.0 

93.4 

114.6 

—21.2 

1896 

102.0 

103.2 

—  1.2 

91.2 

114.2 

—23.0 

1897 

105.0 

103.4 

-f  1.6 

91.2 

113.9 

—22.7 

1898 

106.0 

103.5 

+  2.5 

94.9 

113.5 

—18.6 

1899 

106.7 

103.7 

+  3.0 

101.9 

113.1 

—11.2 

1900 

99.3 

103.9 

—  4.6 

106.9 

112.8 

—  5.9 

1901 

102.3 

104.1 

—  1.8 

110.6 

112.4 

—  1.8 

1902 

103.3 

104.3 

—  1.0 

111.7 

112.0 

—     .3 

1903 

111.7 

104.5 

-+-  7.2 

113.2 

111.6 

+  1.6 

1904 

112.3 

104.7 

+  7.6 

114.2 

111.3 

+  2.9 

1905 

116.3 

104.8 

+  11.5 

117.1 

110.9 

+  6.2 

1906 

113.7 

105.0 

+  8.7 

122.6 

110.5 

+  12.1 

1907 

111.3 

105.2 

+  6.1 

124.9 

110.2 

+  14.7 

1908 

107.7 

105.4 

+  2.3 

126.3 

109.8 

+  16.5 

1909 

108.7 

105.5 

+  3.2 

127.0 

109.4 

+  17.6 

1910 

105.3 

105.7 

—     .4 

129.1 

109.0 

+23.1 

CHAPTER   VI 

SUMMARY  AND  CONCLUSIONS 

These  cycles  of  crops  constitute  the  natural,  material  current 
which  drags  upon  its  surface  the  lagging,  rhythmically  changing 
values  and  prices  with  which  the  economist  is  more  immediately 
concerned. 

The  principal  contribution  of  this  Essay  is  the  dis- 
covery of  the  law  and  cause  of  Economic  Cycles.  The 
rhythm  in  the  activity  of  economic  life,  the  alternation 
of  buoyant,  purposeful  expansion  with  aimless  depres- 
sion, is  caused  by  the  rhythm  in  the  yield  per  acre  of 
the  crops;  while  the  rhythm  in  the  production  of  the 
crops  is,  in  turn,  caused  by  the  rhythm  of  changing 
weather  which  is  represented  by  the  cyclical  changes  in 
the  amount  of  rainfall.  The  law  of  the  cycles  of  rainfall 
is  the  law  of  the  cycles  of  the  crops  and  the  law  of 
Economic  Cycles. 

We  shall  recapitulate  the  main  stages  by  which  this 
conclusion  was  reached  and  shall  take  occasion,  as  the 
stages  are  reviewed,  to  suggest  the  care  that  must 
be  observed  in  interpreting  the  statistical  generaliza- 
tions which  form  the  structure  of  the  argument. 

When  we  begin  to  think  seriously  about  the  cause  of 
Economic  Cycles  we  are  greatly  impressed  by  the  wide 
diffusion  of  these  cyclical  movements  among  the  peoples 
of  the  world,  and  the  inference  appears  to  be  inevitable 
that  there  must  be  some  physical  cause  at  work  to 

135 


136         Economic  Cycles:  Their  Law  and  Cause 

account  for  so  general  a  movement.  As  the  most 
fundamental  need  of  mankind  is  the  need  for  food,  it 
seems  probable  that  the  observed  rhythmical  economic 
changes  may  be  produced  by  the  physical  cause  through 
its  effect  upon  the  food  supply.  If  this  be  so,  then,  as 
the  fluctuations  of  the  food  supply  are  known  to  be 
subject  to  the  supposed  caprices  of  the  weather,  it 
seems  not  unlikely  that  the  physical  cause  may  be  one 
or  more  of  the  elemental  forces  that  are  summarized 
under  the  term  weather.  The  variation  in  the  quantity 
of  the  rainfall  is  one  of  the  weather  changes  known  to 
have  a  marked  effect  upon  the  yield  of  the  crops,  and 
if  this  fact  is  taken  into  consideration  with  the  preceding 
reasoning,  we  have  a  working  theory  as  to  the  cause  of 
Economic  Cycles:  The  changes  in  the  weather  repre- 
sented by  the  changes  in  the  quantity  of  rainfall  cause 
the  changes  in  the  yield  per  acre  of  the  crops,  and  the 
variations  in  the  yield  of  the  crops  cause  the  economic 
changes  known  as  Economic  Cycles.  With  this  work- 
ing theory  in  mind,  we  examined  appropriate  data  with 
reference  to  three  things:  (1)  The  periodicity  of  rain- 
fall; (2)  the  effect  of  rainfall  on  the  crops;  (3)  the  rela- 
tion of  the  yield  of  the  crops  to  Economic  Cycles. 

First,  then,  as  to  the  periodicity  of  rainfall.  The 
problem  as  to  whether  the  quantity  of  rainfall  passes 
through  definite  cycles  involves  two  practical  questions 
that  affect  the  utility  and  the  validity  of  the  results  that 
may  be  attained.  These  questions  are,  first,  as  to  what 
rainfall  data  shall  be  used  in  the  investigation  of  possible 
rainfall  cycles;  and,  second,  as  to  the  method  that  shall 


Sum77iary  and  Conclusions  137 

be  adopted  to  establish  the  existence  of  the  cycles  and 
to  ascertain  their  characteristic  lengths,  amplitudes  and 
phases.  In  our  investigation,  the  choice  of  rainfall  data 
was  suggested  by  the  scope  of  our  general  problem. 
Supposing  that  we  could  find  definite  periods  in  the 
varying  amount  of  the  rainfall,  we  should  then  desire  to 
know  the  relation  of  rainfall  to  the  yield  of  the  crops, 
and  the  relation  of  the  yield  of  the  crops  to  Economic 
Cycles.  It  was  necessary,  therefore,  that  the  data 
of  rainfall  should  refer  to  an  area  in  which  unportant 
crops  are  produced,  and  it  was  desirable  that  the  data  of 
both  rainfall  and  crops  should  refer  to  a  highly  dynamic 
society.  For  these  reasons  we  collected  the  material 
for  our  investigation  from  the  central  part  of  the  United 
States. 

The  method  adopted  in  an  investigation  of  the 
periodicity  of  rainfall  must  satisfy  three  conditions: 
(1)  It  must  exhaust  the  data  in  the  search  for  possible 
cycles;  that  is  to  say,  the  data  must  be  made  to  yield 
all  the  truth  they  contain  relating  to  the  particular 
problem  in  hand.  Frequently  in  the  past,  spurious 
periodicities  have  been  presented  as  real  periodicities, 
chiefly  because  the  investigator  started  with  a  bias  in 
favor  of  a  particular  period  and  did  not  pursue  his 
researches  sufficiently  far  to  determine  whether  his 
result  was  not  one  among  many  spurious,  chance 
periodicities  contained  in  his  material.  In  the  search  for 
real  periodicities  the  data  must  be  exhaustively  ana- 
lyzed. (2)  The  method  must  render  possible  the  dis- 
crimination  between   a   true   periodicity,    having   its 


138         Economic  Cycles:  Their  Law  and  Cause 

origin  in  a  natural  cause  and  persisting  with  a  change  in 
the  samples  of  statistics,  and  a  spurious  periodicity 
which  is  purely  formal,  having  its  origin  in  accidental 
characteristics  of  the  statistical  sample  and  disappear- 
ing, or  radically  altering  its  character,  when  different 
samples  of  statistics  are  made  the  basis  of  the  computa- 
tion. (3)  The  method  must  not  only  make  possible 
the  isolation  of  real  periodicities,  but  it  must  likewise 
enable  one  to  determine  their  essential  characteristics, 
their  length,  phases  and  amplitudes.  The  method  we 
adopted  in  our  researches,  which  is  based  upon  the 
harmonic  analysis,  satisfies  these  three  conditions. 

The  result  of  our  investigation  as  to  the  periodicity  of 
rainfall  in  the  upper  Mississippi  Valley  was  the  dis- 
covery that  the  annual  rainfall  passes  through  two 
cycles  of  approximately  thirty-three  years  and  eight 
years  in  length.  The  amplitude  and  phases  of  these 
two  cycles  were  ascertained,  and  the  equations  to  the 
separate  cycles  were  calculated.  The  two  cycles  were 
then  superposed,  thus  giving  the  general  cyclical  move- 
ment of  rainfall;  the  equation  of  this  compound  cycle 
was  computed  and  the  graph  was  drawn.  It  was  found 
that  the  curve  of  the  rhythmical  movement  of  rainfall 
computed  from  the  equation  to  the  superposed  cycles 
fitted  excellently  well  the  actual  observations  of  rainfall. 
These  results  constitute  the  solution  of  the  first  part  of 
our  general  problem :  Rainfall  in  the  principal  crop  area 
of  the  United  States  passes  through  cycles  of  thirty- 
three  years  and  of  eight  years. 

The  caution  that  should  be  observed  in  the  use  of  our 


Summary  and  Conclusions  139 

conclusions  is  suggested  by  the  method  that  was  em- 
ployed and  the  subject  that  was  investigated.  The 
inquiry  is  a  statistical  study  of  an  aspect  of  meteorology, 
and,  therefore,  the  caution  to  be  exercised  in  the  use 
of  the  conclusions  is  the  caution  that  should  be  applied 
to  statistical  work  in  general  and  to  meteorology  in 
particular.  As  far  as  the  statistical  work  is  concerned, 
it  should  be  observed  that  the  data  were  drawn  from  a 
limited  area  of  the  United  States  and  covered,  at  most, 
seventy-two  years.  Consequently,  while  there  seem  to 
be  very  good  reasons  in  favor  of  the  belief  that,  for  the 
purpose  for  which  they  were  used,  the  data  were  repre- 
sentative of  the  whole  country,  it  is  highly  desirable 
that  similar  studies  should  be  made  for  other  places  and 
other  times.  Furthermore,  the  present  investigation 
was  limited  to  a  study  of  the  periodicity  of  rainfall,  but 
a  more  adequate  research  would  embrace  the  periodicity 
of  temperature  and  of  other  weather  elements,  together 
with  an  investigation  of  the  interrelation  of  the  elements. 
Before  passing  on  to  consider  the  caution  to  be  observed 
in  the  use  of  statistical  studies  of  meteorology,  a  word 
should  be  said  in  justification  of  the  hmitation  of  the 
inquiry  to  the  periodicity  of  annual  rainfall.  The  ob- 
ject of  taking  annual  rainfall  was  to  ascertain  the  mean 
periodicity  of  the  rainfall  of  the  critical  seasons  of  the 
several  crops.  It  would  have  been  more  satisfactory  to 
investigate  the  periodicity  of  the  rainfall  of  the  critical 
season  in  case  of  each  crop,  but,  because  of  the  extreme 
laboriousness  of  the  calculations,  a  device  had  to  be 
adopted  to  limit  the  amount  of  computation. 


140         Economic  Cycles:  Their  Law  arid  Cause 

In  regard  to  the  use  of  statistical  generalizations  in 
meteorology,  we  have  the  cautious  opinion  of  Lord 
Kelvin:  "I  cannot  say  whether  anything  with  reference 
to  Terrestrial  Meteorology  is  done  once  for  all.  I 
think  probably  the  work  will  never  be  done."  There 
is  always  need  of  checking  up  statistical  conclusions  in 
the  light  of  new  data,  and  this  necessity  applies  to  the 
generalization  that  in  the  Mississippi  Valley  the  annual 
rainfall  passes  through  a  double  cycle  of  thirty-three 
years  and  eight  years.  This  conclusion  is  undoubtedly 
warranted  by  the  data  that  lie  at  the  basis  of  the  in- 
vestigation, but  it  would  be  a  grave  fault,  indeed,  to 
hold  that  the  cycles  do  not  alter  with  the  flow  of  time. 
Whether  they  change  or  retain  their  characteristics  can 
be  determined  only  by  accumulating  more  data  than 
are  at  present  available. 

We  come  now  to  the  second  part  of  our  general 
problem,  namely,  to  the  consideration  of  the  relation 
between  rainfall  and  the  yield  of  the  crops,  and  again 
the  questions  of  data  and  method  must  be  settled. 
In  choosing  the  data,  the  prime  consideration  was  to 
make  sure  that  the  crops  selected  should  be  representa- 
tive of  the  conditions  of  crop-producing  in  the  Middle 
West.  The  five  principal  crops  in  the  Middle  West  are 
corn,  hay,  wheat,  oats,  and  potatoes,  and  of  these  five 
all  except  wheat  were  taken  to  serve  as  representative 
crops.  Wheat  was  omitted  because  of  technical  dif- 
ficulties: First,  it  is  impossible,  except  for  recent  years, 
to  separate  in  the  published  statistics  the  yield  per  acre 


Summary  and  Conclusions  141 

of  spring  wheat  from  the  yield  of  winter  wheat;  and, 
secondly,  since  the  growth  seasons  and  critical  periods 
of  these  two  varieties  of  wheat  are  different,  it  seemed 
unwise  to  attempt  to  connect  the  rainfall  of  any  season 
with  the  yield  per  acre  of  wheat  in  which  the  figures  for 
the  yield  referred  to  spring  and  winter  wheat  taken 
together.  For  these  reasons  the  representative  crops 
were  Umited  to  corn,  hay,  oats,  and  potatoes;  and  the 
yield  per  acre  of  these  several  crops  throughout  a  long 
period  of  time,  together  with  the  rainfall  of  their 
respective  critical  seasons,  form  the  numerical  data  of 
the  investigation. 

The  method  of  determining  the  critical  seasons  was  to 
find,  by  the  use  of  the  statistical  theory  of  correlation, 
the  month  or  months,  in  the  lifetime  of  the  several 
crops,  the  rainfall  of  which  gave  the  highest  correlation 
with  the  ultmiate  yield.  This  preliminary  inquiry 
afforded  a  partial  answer  to  our  general  question  as  to 
the  relation  between  rainfall  and  the  crops.  We  found 
that  in  case  of  each  of  the  crops  the  yield  per  acre  is 
directly  connected  with  the  rainfall  of  some  critical 
period,  and  in  all  of  the  crops  except  oats  the  connection 
is  very  close.  It  seemed  probable,  therefore,  that  since 
the  rainfall  passes  through  definite  cycles,  and  since 
the  yield  per  acre  of  the  crops  is  intimately  related  with 
the  rainfall  of  their  respective  critical  seasons,  the  yield 
per  acre  of  the  crops  should  likewise  pass  through  the 
double  cycle  described  by  the  rainfall  of  the  critical 
seasons. 

The  investigation  of  the  relation  of  the  cycles  of  the 


142         Economic  Cycles:  Their  Law  and  Cause 

crops  to  the  cycles  of  the  rainfall  of  the  critical  seasons 
was  carried  out  in  two  ways,  first  for  the  crops  taken 
singly,  and  then  for  the  crops  taken  all  together.  In  the 
inquiry  relating  to  the  separate  crops,  the  equations  to 
the  double  cycle  in  the  yield  per  acre  and  to  the  double 
cycle  in  the  rainfall  of  the  corresponding  critical  seasons 
were  computed,  and  the  graphs  were  drawn.  When  the 
graphs  of  the  cycles  of  the  crops  were  superposed  upon 
the  graphs  of  the  cycles  of  rainfall  of  the  respective 
critical  seasons,  the  two  curves  were  found  to  present  a 
very  remarkable  congruence.  In  the  inquiry  relating 
to  the  crops  taken  all  together,  an  index  number  of  the 
yield  per  acre  of  the  crops  and  an  index  number  of  the 
mean  effective  rainfall  of  the  critical  seasons  were  con- 
structed. The  equations  to  the  double  cycle  in  both 
indices  were  computed,  their  graphs  were  drawn  and 
then  superposed.  It  was  found  that  the  characteristic 
features  of  the  rainfall  curve  were  reproduced  in  the 
curve  of  the  index  number  of  the  yield  per  acre  of  the 
crops. 

These  results,  referring  both  to  the  crops  taken  singly 
and  to  the  crops  taken  all  together,  are  the  answers  to 
the  second  part  of  our  general  question:  The  yield  per 
acre  of  the  representative  crops  is  closely  connected 
statistically  with  the  rainfall  of  the  respective  critical 
seasons,  and  the  relation  is  so  close  that  the  cycles  of 
the  yield  per  acre  of  the  crops  reproduce  in  char- 
acteristic ways  the  cycles  of  the  rainfall  of  the  critical 
seasons.  The  fundamental,  persistent  cause  of  the 
cycles  of  crops  is,  therefore,  the  rhythmical  movement 


Summary  and  Conclusions  143 

in  the  conditions  of  the  weather  represented  by  the 
cycles  in  the  amount  of  rainfall. 

In  the  cautious  use  of  the  preceding  generalizations, 
one  will  bear  in  mind  that  only  four  crops  have  been 
investigated,  and  that,  in  ascertaining  the  critical 
seasons,  the  monthly  rainfall  has  been  used.  The 
critical  seaons  could  undoubtedly  be  determined  more 
accurately  if  the  figures  for  the  weekly  rainfall  were 
employed.  Furthermore,  the  inquiry  has  been  limited 
to  the  relation  of  the  yield  of  the  crops  to  rainfall, 
whereas  a  more  adequate  study  would  include  at  least 
the  effects  of  temperature. 

Thus  far  the  investigation  has  established  the  law 
and  cause  of  the  cycles  of  the  crops:  The  cause  of  the 
cycles  in  the  physical  productivity  of  the  crops  is  the 
cyclical  variation  of  the  weather  represented  by  the 
cycles  of  rainfall,  and  the  law  of  the  cycles  of  rainfall  is 
the  law  of  the  cycles  of  the  crops.  In  order  to  bring 
these  physical  results  into  relation  with  the  rhythmical 
movements  of  prices  and  values,  we  had  first  to  show 
how  the  prices  of  the  several  crops  vary  with  their 
respective  supplies.  In  technical  terms,  we  had  to 
discover  the  laws  of  demand  for  the  individual  crops. 

The  equations  to  the  law  of  demand  for  corn,  hay, 
oats,  and  potatoes  were  computed,  and  the  graphs  were 
drawn.  The  degree  of  precision  with  which  these 
demand  curves  might  be  used  as  formulae  for  predicting 
prices  was  ascertained,  and  the  coefficients  of  the 
elasticity  of  demand  for  the  representative  commodities 


144         Economic  Cycles:  Their  Law  and  Cause 

were  calculated.  The  equations  to  the  law  of  demand 
for  all  four  crops  conformed  to  a  single  type,  indicating 
that  as  the  supply  of  the  commodity  increases,  the  price 
falls.  For  reasons  that  were  explained  in  the  discussion, 
we  named  this  type  of  demand  curve  the  negative  type. 

It  will  be  recalled  that  the  three  divisions  of  our 
general  problem  were  (1)  the  periodicity  of  rainfall; 
(2)  the  effect  of  rainfall  upon  the  crops;  and  (3)  the 
relation  of  the  yield  of  the  crops  to  Economic  Cycles. 
The  elaboration  of  a  method  for  calculating  the  demand 
curves  placed  us  in  position  to  examine  the  third  and 
final  part  of  the  problem.  The  law  of  demand  for  the 
crops  connects  the  price  of  the  several  crops  with  their 
respective  supplies,  but  the  supply  is  dependent  upon 
both  the  yield  per  acre  and  the  extent  of  the  acreage. 
In  order  to  bring  our  findings  with  regard  to  the  period- 
icity in  the  yield  per  acre  into  relation  with  prices  and 
values,  it  is  clear  that  we  must  know  the  relation 
between  the  variation  in  the  price  of  the  commodity 
and  the  yield  per  acre  of  the  commodity.  This  ques- 
tion we  examined  at  length,  and  found  the  tie  between 
price  and  yield  per  acre  to  be  as  close  as  the  tie  between 
price  and  supply.  To  differentiate  between  demand 
curves  and  curves  showing  the  relation  between  yield 
per  acre  and  price,  we  called  the  latter  curves,  yield- 
price  curves.  We  deduced  the  equations  to  the  yield- 
price  curves  for  the  four  representative  commodities 
and  measured  the  degree  of  precision  with  which  their 
equations   might   be  used  as  formulae  for  predicting 


Summary  and  Conclusions  145 

prices.  In  all  of  these  relations,  the  yield-price  curves 
were  found  to  be  as  accurate  and  as  satisfactory  as 
the  demand  curves  themselves. 

With  the  possession  of  the  yield-price  curves,  showing 
the  relation  between  the  prices  of  the  crops  and  their 
varying  yield  per  acre,  it  might  seem  that  the  problem 
of  agricultural  cycles  at  least  was  completely  elucidated. 
As  we  know  how  the  periodicity  in  the  yield  of  the  crops 
follows  upon  the  periodicity  in  the  rainfall,  and  how  the 
prices  vary  with  the  yield,  one  might  conclude  that 
the  course  of  prices  could  be  predicted  for  a  long  time. 
The  inference  would  be  entirely  true  but  for  the  fact 
that  the  demand  curves  and  the  yield-price  curves  move 
alternately  up  and  down  with  the  flow  of  time.  This 
complication  made  it  necessary  to  investigate  the 
rhythmical  movement  of  the  yield-price  curves,  and 
we  found  that  the  demand  curves,  or  yield-price  curves, 
rise  or  fall  with  the  level  of  general  prices  and  with  the 
level  of  the  index  of  the  yield  per  acre  of  the  crops. 

The  preceding  facts  seemed  to  involve  a  contradiction 
with  an  a  priori  doctrine  of  theoretical  economics. 
According  to  the  economic  dogma  of  the  uniformity  of 
the  demand  function,  all  demand  curves  are  of  the 
negative  type:  As  the  amount  of  the  commodity  in- 
creases, the  price  falls.  But  if  this  be  true,  how  is  it 
possible  for  a  fall  of  general  prices  to  accompany  a  fall 
in  the  index  of  the  yield  per  acre  of  the  crops?  If  the 
yield  per  acre  of  the  crops  decreases,  then,  according  to 
the  yield-price  curves  and  the  demand  curves,  the  price 
of  the  crops  will  rise.    Moreover,  as  the  profits  of  trade 


146         Economic  Cycles:  Their  Law  and  Cause 

and  commerce  are  largely  dependent  upon  the  volume 
of  the  crops,  it  seems  likely  that  the  demand  for  general 
commodities  would  decrease  with  a  deficiency  in  the 
harvests,  and,  according  to  the  dogma  of  the  uniformity 
of  the  demand  function,  the  prices  of  general  commodi- 
ties should  rise.  The  ultimate  result  of  bad  harvests, 
therefore,  would  be  a  rise  in  general  prices.  The  facts, 
however,  bear  out  the  contrary  view.  General  prices 
fall  with  a  decrease  in  the  yield  per  acre  of  the  crops. 
A  consideration  of  this  difficulty  led  to  the  discovery 
that  there  is  a  positive  type  of  demand  curve  as  well  as  a 
negative  type.  For  a  representative  producer's  good, 
for  example  pig-iron,  the  law  of  demand  is  such  that  as 
the  amount  of  commodity  increases  the  price  of  the 
commodity  rises,  and  as  the  amount  of  the  commodity 
decreases  the  price  of  the  commodity  falls.  The  exist- 
ence of  both  positive  and  negative  types  of  demand  in  a 
highly  dynamic  society  suggested  a  working  theory 
which  seemed  to  account  for  the  interrelation  of  all 
the  known  relevant  facts,  and  which  may  be  stated  in 
compact  form.  The  rhythmically  varying  yield  per 
acre  of  the  crops  is  the  cause  of  Economic  Cycles: 
When  the  yield  increases,  the  volume  of  trade,  the 
activity  of  industry  and  the  amount  of  employment 
increase;  the  demand  for  producers'  goods  increases  and 
the  prices  of  producers'  goods  rise;  the  demand  curves 
for  agricultural  commodities  rise;  with  the  ultimate 
result  of  a  rise  of  general  prices.  The  contrary  changes 
would  follow  upon  a  fall  in  the  yield  per  acre  of  the 
crops. 


Summary  and  Conclusions  147 

Beyond  what  we  had  ah-eady  established,  this  theory 
of  the  interrelation  of  economic  changes  required  for 
its  complete  demonstration  the  proof  of  the  existence  of 
two  fundamental  relations,  to  wit,  that  the  cycles  in  the 
yield  per  acre  of  the  crops  are  reproduced 

(1)  in  the  activity  of  general  industry; 

(2)  in  the  movement  of  general  prices. 

In  order  to  test  whether  these  relations  actually  exist, 
an  index  number  of  the  yield  per  acre  of  the  crops  was 
constructed  for  the  nine  crops,  corn,  wheat,  oats,  barley, 
rye,  buckwheat,  hay,  cotton,  and  potatoes.  To  make 
sure  of  keeping  close  to  the  results  already  established 
for  the  representative  commodities  corn,  hay,  oats,  and 
potatoes,  the  correlation  of  the  index  of  the  nine  crops 
with  the  index  of  the  four  representative  crops  was 
computed  and  found  to  be  r  =  .960. 

As  the  production  of  pig-iron  is  generally  regarded  as 
a  good  "barometer"  of  the  activity  of  industry,  we 
sought  an  answer  to  the  above  first  question  by  in- 
vestigating whether  the  cycles  in  the  yield  per  acre  of 
the  nine  crops  were  reproduced  in  the  cycles  in  the 
production  of  pig-iron.  The  inquiry  involved  the 
problems  of  the  separation  of  the  cyclical  and  the  secular 
movements  in  the  production  of  pig-iron,  and  the 
ascertainment  of  the  amount  of  the  lag  in  the  cycles 
of  pig-iron  behind  the  cycles  in  the  yield  per  acre  of  the 
crops.  We  found  that  it  takes  between  one  and  two 
years  for  the  stimulation  of  increasing  harvests  to  work 
out  its  maximum  effect  in  promoting  the  activity  of 
industry  as  that  activity  is  represented  in  the  ''barom- 


148         Economic  Cycles:  Their  Law  and  Cause 

eter"  of  industry,  the  production  of  pig-iron;  and 
that,  when  an  allowance  is  made  for  a  lag  of  two  years 
in  the  adjustment  of  the  pig-iron  industry,  the  cycles 
of  the  yield  per  acre  of  the  crops  are  generally  repro- 
duced in  the  cycles  of  the  production  of  pig-iron,  the 
relation  being  so  close  that  the  coefficient  of  correlation 
is  r  =  .718. 

To  find  the  relation  of  the  cycles  in  the  yield  per  acre 
of  the  crops  to  the  cycles  in  the  movement  of  general 
prices,  we  made  use  of  an  index  number  of  general 
prices  extending  from  1870  to  1910,  and  of  our  index 
number  of  the  yield  per  acre  of  nine  crops  covering  the 
same  interval  of  time.  The  problem  of  separating  the 
cyclical  movements  in  these  two  series  from  their 
secular  movements  was  solved,  and  the  lag  of  the  cycles 
of  general  prices  behind  the  cycles  in  the  yield  of  crops 
was  found  to  be  about  four  years.  The  coefficient  of 
correlation  between  the  cycles  in  the  yield  of  the  crops 
and  the  cycles  in  the  general  prices  lagging  four  years 
behind  the  crop  cycles  reached  the  very  high  value 
r  =  .800.  When  the  lagging  cycles  of  general  prices  were 
plotted  and  their  graph  superposed  upon  the  graph  of 
the  cycles  in  the  yield  per  acre  of  the  crops,  the  two 
curves  were  found  to  present  a  degree  of  congruence  so 
close  as  to  justify  our  working  theory  that  the  fun- 
damental, persistent  cause  of  the  cycles  of  prices  is  the 
rhythmical  movement  in  the  yield  per  acre  of  the  crops. 
The  cycles  in  the  yield  per  acre  of  the  crops  are  followed 
at  an  interval  of  about  two  years  by  the  cycles  in  the 


Summary  and  Conclusions  149 

activity  of  industry  and  of  the  volume  of  trade,  and  at 
an  interval  of  about  four  years  in  the  cycles  of  prices. 
These  conclusions  brought  to  a  close  the  last  part  of 
our  general  problem  of  the  cause  and  law  of  Economic 
Cycles. 

The  links  in  the  sequence  of  causation  were  com- 
pletely estabhshed:  The  fundamental,  persistent  cause 
of  the  cycles  in  the  yield  of  the  crops  is  the  cyclical 
movement  in  the  weather  conditions  represented  by  the 
rhythmically  changing  amount  of  rainfall;  the  cycUcal 
movement  in  the  yield  of  the  crops  is  the  fundamental, 
persistent  cause  of  Economic  Cycles. 

In  the  Introduction  to  this  Essay  it  was  observed  that 
economic  dynamics  stands  in  need  of  a  law  that  shall 
be  to  a  changing  society  what  the  law  of  diminishing 
returns  is  to  a  society  in  a  relatively  static  state.  We 
may  now  formulate  the  law:  The  weather  conditions 
represented  by  the  rainfall  in  the  central  part  of  the 
United  States,  and  probably  in  other  continental  areas, 
pass  through  cycles  of  approximately  thirty-three  years 
and  eight  years  in  duration,  causing  like  cycles  in  the 
yield  per  acre  of  the  crops;  these  cycles  of  crops  con- 
stitute the  natural,  material  current  which  drags  upon 
its  surface  the  lagging,  rhythmically  changing  values 
and  prices  with  which  the  economist  is  more  immedi- 
ately concerned. 


T 


HE  following  pages  contain  advertisements 'of  jMac 
millan  books  bv  the  same  author. 


LAWS  OF  WAGES 

AN  ESSAY  IN  STATISTICAL  ECONOMICS 
By  Henry  Ludwell  Moore 

Professor  of  Political  Economy  in 
Columbia  University 

Cloth,  SI. 60,  net. 

Extract  from  the  Introduction:  "In  the  following  chapters 
I  have  endeavored  to  use  the  newer  statistical  methods  and 
the  more  recent  economic  theory  to  extract,  from  data  re- 
lating to  wages,  either  new  truth  or  else  truth  in  such  new 
form  as  will  admit  of  its  being  brought  into  fruitful  relations 
with  the  generahzations  of  economic  science." 

CONTENTS 

PAGE 

Introduction 1 

Chapter  I 

Statistical  Laws 

A  Scatter  Diagram 11 

Definition  of  Terms 15 

Characteristics  of  Statistical  Laws 21 

Chapter  II 

Wages,  Means  of  Subsiste7ice,  and  the  Standard  of  Life 

Description  of  Data 26 

Wages  and  the  Means  of  Subsistence 29 

Wages  and  the  Standard  of  Life 33 

Wages  of  Skilled  and  of  Unskilled  Laborers 39 

Chapter  III 

Wages  and  the  Productivity  of  Labor 

Description  of  Data 45 

Fluctuations  in  the  Rate  of  Wages  and  in  the  Value  of  the  Product    46 

(over) 


LAWS  OF  WAGES  by  Henry  Ludwell  Moore— Continued 

CO^^TE^iTS— Continued  page 

Fluctuations  in  the  Laborer's  Relative  Share  of  the  Product  and  in 

the  Ratio  of  Capital  to  Labor 55 

The  General  Trend  of  Wages 61 


Ch-'vpter  IV 

Wages  and  Ability 

An  Hypothesis  as  to  the  Distribution  of  AbiUty 74 

Grounds  for  the  Hypothesis 76 

The  Expression  of  the  Gaussian  Law  in  a  Form  that  will  facihtate 

the  Testing  of  the  Differential  Theory  of  Wages 78 

The  Standard  Population 82 

The  Apphcation  of  the  Theory  of  the  Standard  Population 85 

Remark  upon  the  Preceding  Demonstration 93 

Chapter  V 

Wages  and  Strikes 

Outcome  of  Strikes  as  affected  by  the  Strength  of  Trades-Unions  105 

Outcome  of  Strikes  as  limited  by  Economic  Law 121 

Summary 134 

Chapter  VI 

Wages  and  the  Concentration  of  Industry 

Wages  as  affected  by  the  Concentration  of  Industry 140 

Amount  of  Employment 153 

Continuity  of  Employment 156 

Length  of  Working  Day 161 

Chapter  VII 

Conclusions 

Statistical  Economics  and  Industrial  Legislation 169 

Practical  Aspects  of  the  Results  of  Preceding  Chapters 174 

Statistical  Economics  and  Synthetic  Economics 196 

COMMENTS  OF  SPECIALISTS 

"Professor  Moore  brings  to  his  task  a  wide  acquaintance  with  the 
most  difficult  parts  of  the  literature  of  economics  and  statistics,  a  full 
appreciation  of  its  large  problems,  a  judicial  spirit  and  a  dignified  style." 
F.  W.  Taussig,  in  the  Quarterly  Journal  of  Economics. 

"Statistics  of  the  ordinary  official  kind  have  often  served  to  support 
the  arguments  of  poUtical  economists.  But  this  is  the  first  time,  we 
believe,  that  the  higher  statistics,  which  arc  founded  on  the  Calculus  of 


LAWS  OF  WAGES  by  Henry  Ludwell  Moore— Continued 

Probabilities,  have  been  used  on  a  large  scale  as  a  buttress  of  economic 
theory."    F.  Y.  Edgeworth,  in  the  Economic  Journal. 


"Professor  Moore  has  broken  new  ground  in  a  most  interesting  field, 
and  while  we  may  differ  from  him  in  the  weight  to  be  attached  to  this 
or  that  result  or  the  interpretation  to  be  placed  on  some  observed  co- 
efficient, we  may  offer  cordial  congi-atulations  on  the  work  as  a  whole. 
G.  U.  Yule,  in  the  Journal  of  the  Royal  Statistical  Society. 

"Die  Fruchtbarkeit  der  verwendeten  Methode  scheint  mir  dm-ch 
diese  Untersuchungen  zweifeUos  erwiesen,  ebenso  wie  die  Erreichbarkeit 
des  Ziels,  die  Theorie  ganz  dicht  an  die  Zahlenausdriicke  der  wu-tschaft- 
Hchen  Tatsachen  heranzubringen.  Und  das  ist  eine  Tat,  zu  der  der  Autor 
nur  zu  begliickwijnschen  ist.  .  .  .  Hat  das  Buch  auch  auf  der  Hand 
liegende  Fehler — in  der  Zukunft  wird  man  sich  seiner  als  der  ersten 
klaren,  einfachen  und  zielbewussten  Darlegung  und  Exemplifizierung  der 
Anwendung  der  '  hoheren  Statistik '  auf  okonomische  Problerae  dankbar 
erinnern."  Joseph  Schumpeter,  in  the  Archiv  fur  Sozialwissenschaft 
und  Sozialpolitik. 

"Non  seulement  il  nous  enseigne  I'emploi  d'une  methode  qui  dans  de 
certaines  Umites  pent  etre  tres  feconde.  Mais  encore  son  habilet6 
personnelle  dans  le  maniement  de  cette  methode  est  tres  r^elle.  II  sait 
scruter  les  statistiques  d'une  fa^on  fort  penetrante  et  exposer  les  re- 
sultats  de  ses  recherches  avec  beaucoup  d'elegance.  Le  lecteur  frangais 
en  particulier,  appreciera  I'ingeniosit^  avec  laquelle  il  tire  des  statistiques 
frangaises  des  inductions  souvent  nouvelles  et  justes."  Albert  Afta- 
LiON,  in  the  Revue  d'hisloire  des  doctrines  economiques. 

"Alcuni  dei  risultati  ottenuti  dall'autore,  sono  nuovi  e  suggestivi 
e  da  essi  molte  conclusioni  si  possono  trarre  (cui  I'autore  accenna  nel 
capitolo  finale  della  sua  opera)  sia  rispetto  alle  teorie  del  salario  che 
rispetto  alia  politica  sociale.  II  libro  e  insomma,  ripetiamo,  un  con- 
tribute molto  importante  all'investigazione  scientifica  dei  fenomeni 
economici  e  vorremmo  che  esso  stimolasse  parecchi  altri  studiosi  a  fare 
per  altre  Industrie  o  per  altri  paesi,  recerche  analoghe.  Constantino 
Bresciani  Turroni,  in  the  Giomale  degli  Economisti. 


THE   MACMILLAN  COMPANY 

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